Tootfinder

Automata-Theoretic Characterisations of Branching-Time Temporal Logics
Massimo Benerecetti, Laura Bozzelli, Fabio Mogavero, Adriano Peron
https://arxiv.org/abs/2404.17421

Automata-Theoretic Characterisations of Branching-Time Temporal Logics
Characterisations theorems serve as important tools in model theory and can be used to assess and compare the expressive power of temporal languages used for the specification and verification of properties in formal methods. While complete connections have been established for the linear-time case between temporal logics, predicate logics, algebraic models, and automata, the situation in the branching-time case remains considerably more fragmented. In this work, we provide an automata-theoreti…

Local stochastic computing using memristor-enabled stochastic logics
Lekai Song, Pengyu Liu, Jingfang Pei, Yang Liu, Songwei Liu, Shengbo Wang, Leonard W. T. Ng, Tawfique Hasan, Kong-Pang Pun, Shuo Gao, Guohua Hu
https://arxiv.org/abs/2402.16908

Local stochastic computing using memristor-enabled stochastic logics
Stochastic computing offers a probabilistic approach to address challenges posed by problems with uncertainty and noise in various fields, particularly machine learning. The realization of stochastic computing, however, faces the limitation of developing reliable stochastic logics. Here, we present stochastic logics development using memristors. Specifically, we integrate memristors into logic circuits to design the stochastic logics, wherein the inherent stochasticity in memristor switching is…

«Models All The Way Down» is a really interesting exploration of how an image data set (in this case LAION-5B) was assembled to be used for training ML/"AI" models!
> "It contains less about how humans see the world than it does about how search engines see the world. It is a dataset that is powerfully shaped by commercial logics."
https://knowingmachines.org/models-all-the-way

On Some Infinitary Logics
Jouko Vaananen, Boban Velickovic
https://arxiv.org/abs/2402.13344 https://arxiv.org/pdf/2402.13344

On Some Infinitary Logics
We define a new class of infinitary logics $\mathscr L^1_{κ,α}$ generalizing Shelah's logic $\mathbb L^1_κ$ defined in \cite{MR2869022}. If $κ=\beth_κ$ and $α<κ$ is infinite then our logic coincides with $\mathbb L^1_κ$. We study the relation between these logics for different parameters $κ$ and $α$. We give many examples of classes of structures that can or cannot be defined in these logics. Finally, we give a different version of Lindström's Theorem for $\mathbb L^1_κ$ in terms of…

This https://arxiv.org/abs/2204.07839 has been replaced.
link: https://scholar.google.com/scholar?q=a

Dependence Logics in Temporal Settings
Many forms of dependence manifest themselves over time, with behavior of variables in dynamical systems as a paradigmatic example. This paper studies temporal dependence in dynamical systems from a logical perspective, by enriching a minimal modal base logic of static functional dependencies. We first introduce a logic for dynamical systems featuring temporalized variables, provide a complete axiomatic proof calculus, and show that its satisfiability problem is decidable. Then, to capture expli…

This https://arxiv.org/abs/2302.13734 has been replaced.
initial toot: https://mastoxiv.page/@a…

Gate-control of superconducting current: mechanisms, parameters and technological potential
In conventional metal-oxide semiconductor (CMOS) electronics, the logic state of a device is set by a gate voltage (VG). The superconducting equivalent of such effect had remained unknown until it was recently shown that a VG can tune the superconducting current (supercurrent) flowing through a nanoconstriction in a superconductor. This gate-controlled supercurrent (GCS) effect can lead to superconducting logics like CMOS logics, but with lower energy dissipation. The physical mechanism underly…

This https://arxiv.org/abs/2204.07839 has been replaced.
link: https://scholar.google.com/scholar?q=a

Dependence Logics in Temporal Settings
Many forms of dependence manifest themselves over time, with behavior of variables in dynamical systems as a paradigmatic example. This paper studies temporal dependence in dynamical systems from a logical perspective, by enriching a minimal modal base logic of static functional dependencies. We first introduce a logic for dynamical systems featuring temporalized variables, provide a complete axiomatic proof calculus, and show that its satisfiability problem is decidable. Then, to capture expli…

This https://arxiv.org/abs/2307.14826 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Graded Semantics and Graded Logics for Eilenberg-Moore Coalgebras
Coalgebra, as the abstract study of state-based systems, comes naturally equipped with a notion of behavioural equivalence that identifies states exhibiting the same behaviour. In many cases, however, this equivalence is finer than the intended semantics. Particularly in automata theory, behavioural equivalence of nondeterministic automata is essentially bisimilarity, and thus does not coincide with language equivalence. Language equivalence can be captured as behavioural equivalence on the det…

@… @… I take “bureaucracy” as an analytical description of a kind of organization, its logics, materiality, cultures, effects, etc., not as an evaluation of organizational life. See @…

This https://arxiv.org/abs/2307.00831 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the Satisfiability of Local First-Order Logics with Data
We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain. Data values can be compared wrt.\ equality. As the satisfiability problem for this logic is undecidable in general, we introduce a family of local fragments. They restrict quantification to the neighbourhood of a given reference point that is bounded by some radius. Our first main result establishes decidability of the satisfiability problem for the local radius-1 fr…

Two-layered logics for probabilities and belief functions over Belnap--Dunn logic
Marta Bilkova, Sabine Frittella, Daniil Kozhemiachenko, Ondrej Majer
https://arxiv.org/abs/2402.12953

Two-layered logics for probabilities and belief functions over Belnap--Dunn logic
This paper is an extended version of an earlier submission to WoLLIC 2023. We discuss two-layered logics formalising reasoning with probabilities and belief functions that combine the Lukasiewicz $[0,1]$-valued logic with Baaz $\triangle$ operator and the Belnap--Dunn logic. We consider two probabilistic logics that present two perspectives on the probabilities in the Belnap--Dunn logic: $\pm$-probabilities and $\mathbf{4}$-probabilities. In the first case, every event $ϕ$ has independent posi…

On Propositional Dynamic Logic and Concurrency
Matteo Acclavio, Fabrizio Montesi, Marco Peressotti
https://arxiv.org/abs/2403.18508 https://

On Propositional Dynamic Logic and Concurrency
Dynamic logic in the setting of concurrency has proved problematic because of the challenge of capturing interleaving. This challenge stems from the fact that the operational semantics for programs considered in these logics is tailored on trace reasoning for sequential programs. In this work, we generalise propositional dynamic logic (PDL) to a logic framework we call operational propositional dynamic logic (OPDL) in which we are able to reason on sets of programs provided with arbitrary opera…

On Propositional Dynamic Logic and Concurrency
Matteo Acclavio, Fabrizio Montesi, Marco Peressotti
https://arxiv.org/abs/2403.18508 https://

On Propositional Dynamic Logic and Concurrency
Dynamic logic in the setting of concurrency has proved problematic because of the challenge of capturing interleaving. This challenge stems from the fact that the operational semantics for programs considered in these logics is tailored on trace reasoning for sequential programs. In this work, we generalise propositional dynamic logic (PDL) to a logic framework we call operational propositional dynamic logic (OPDL) in which we are able to reason on sets of programs provided with arbitrary opera…

This https://arxiv.org/abs/2401.03265 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Finite Hilbert systems for Weak Kleene logics
Multiple-conclusion Hilbert-style systems allow us to finitely axiomatize every logic defined by a finite matrix. Having obtained such axiomatizations for Paraconsistent Weak Kleene and Bochvar-Kleene logics, we modify them by replacing the multiple-conclusion rules with carefully selected single-conclusion ones. In this way we manage to introduce the first finite Hilbert-style single-conclusion axiomatizations for these logics.

Unifying Asynchronous Logics for Hyperproperties
Alberto Bombardelli, Laura Bozzelli, C\'esar S\'anchez, Stefano Tonetta
https://arxiv.org/abs/2404.16778

Unifying Asynchronous Logics for Hyperproperties
We introduce and investigate a powerful hyper logical framework in the linear-time setting, we call generalized HyperLTL with stuttering and contexts (GHyperLTL_SC for short). GHyperLTL_SC unifies known asynchronous extensions of HyperLTL and the well-known extension KLTL of LTL with knowledge modalities under both the synchronous and asynchronous perfect recall semantics. As a main contribution, we individuate a meaningful fragment of GHyperLTL_SC, we call simple GHyperLTL_SC, with a decidable…

Forcing, Transition Algebras, and Calculi
Hashimoto Go, Daniel G\u{a}in\u{a}, Ionu\c{t} \c{T}u\c{t}u
https://arxiv.org/abs/2404.16111 https://

Forcing, Transition Algebras, and Calculi
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition relations, which are treated similarly to the actions used in dynamic logics in order to define necessity and possibility operators. This leads to a higher degree of expressivity than that of many-sorted first-order logic. For example, one can finitely axiomatize both…

This https://arxiv.org/abs/2401.03265 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Finite Hilbert systems for Weak Kleene logics
Multiple-conclusion Hilbert-style systems allow us to finitely axiomatize every logic defined by a finite matrix. Having obtained such axiomatizations for Paraconsistent Weak Kleene and Bochvar-Kleene logics, we modify them by replacing the multiple-conclusion rules with carefully selected single-conclusion ones. In this way we manage to introduce the first finite Hilbert-style single-conclusion axiomatizations for these logics.

Lars Birkedal has updated us with all the greatest and newest in iris/separation logics for proving correspondence and almost sure termination of probabilistic programs.
I promise to spam you less after this keynote. Want to keep some of my attention on the conference.
#etaps #etaps2024

Verifiably Following Complex Robot Instructions with Foundation Models
Benedict Quartey, Eric Rosen, Stefanie Tellex, George Konidaris
https://arxiv.org/abs/2402.11498

Verifiably Following Complex Robot Instructions with Foundation Models
Enabling robots to follow complex natural language instructions is an important yet challenging problem. People want to flexibly express constraints, refer to arbitrary landmarks and verify behavior when instructing robots. Conversely, robots must disambiguate human instructions into specifications and ground instruction referents in the real world. We propose Language Instruction grounding for Motion Planning (LIMP), a system that leverages foundation models and temporal logics to generate ins…

Formal Synthesis of Controllers for Safety-Critical Autonomous Systems: Developments and Challenges
Xiang Yin, Bingzhao Gao, Xiao Yu
https://arxiv.org/abs/2402.13075

Formal Synthesis of Controllers for Safety-Critical Autonomous Systems: Developments and Challenges
In recent years, formal methods have been extensively used in the design of autonomous systems. By employing mathematically rigorous techniques, formal methods can provide fully automated reasoning processes with provable safety guarantees for complex dynamic systems with intricate interactions between continuous dynamics and discrete logics. This paper provides a comprehensive review of formal controller synthesis techniques for safety-critical autonomous systems. Specifically, we categorize t…

Topological product of modal logics with the McKinsey axiom
Andrey Kudinov
https://arxiv.org/abs/2403.06334 https://arxiv.org/pdf/240…

Topological product of modal logics with the McKinsey axiom
In this paper we consider the topological products of modal logics of S4.1 and S4. We prove that it is equal to the fusion of logics S4.1 and S4 plus one additional axiom. We also show that this product is decidable. This is an example of a topological product of logics that is greater than the fusion but less than the expanding product of the corresponding logics.

Fully Evaluated Left-Sequential Logics
Alban Ponse, Daan J. C. Staudt
https://arxiv.org/abs/2403.14576 https://arxiv.org/pdf/2403.145…

Fully Evaluated Left-Sequential Logics
We consider a family of two-valued "fully evaluated left-sequential logics" (FELs), of which Free FEL (defined by Staudt in 2012) is most distinguishing (weakest) and immune to atomic side effects. Next is Memorising FEL, in which evaluations of subexpressions are memorised. The following stronger logic is Conditional FEL (inspired by Guzmán and Squier's Conditional logic, 1990). The strongest FEL is static FEL, a sequential version of propositional logic. We use evaluation trees as a simple, …

This https://arxiv.org/abs/2401.10056 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Axiomatization of Boolean Connexive Logics with syncategorematic negation and modalities
In the article we investigate three classes of extended Boolean Connexive Logics. Two of them are extensions of Modal and non-Modal Boolean Connexive Logics with a property of closure under an arbitrary number of negations. The remaining one is an extension of Modal Boolean Connexive Logic with a property of closure under the function of demodalization. In our work we provide a formal presentation of mentioned properties and axiom schemata that allow us to incorporate them into Hilbert-style ca…

Predictable Verification using Intrinsic Definitions
Adithya Murali, Cody Rivera, P. Madhusudan
https://arxiv.org/abs/2404.04515 https://

Predictable Verification using Intrinsic Definitions
We propose a novel mechanism of defining data structures using intrinsic definitions that avoids recursion and instead utilizes monadic maps satisfying local conditions. We show that intrinsic definitions are a powerful mechanism that can capture a variety of data structures naturally. We show that they also enable a predictable verification methodology that allows engineers to write ghost code to update monadic maps and perform verification using reduction to decidable logics. We evaluate our …

Semi-Substructural Logics with Additives
Niccol\`o Veltri (Tallinn University of Technology), Cheng-Syuan Wan (Tallinn University of Technology)
https://arxiv.org/abs/2404.14922 <…

Semi-Substructural Logics with Additives
This work concerns the proof theory of (left) skew monoidal categories and their variants (e.g. closed monoidal, symmetric monoidal), continuing the line of work initiated in recent years by Uustalu et al. Skew monoidal categories are a weak version of Mac Lane's monoidal categories, where the structural laws are not required to be invertible, they are merely natural transformations with a specific orientation. Sequent calculi which can be modelled in such categories can be identified as deduc…

This https://arxiv.org/abs/2401.10056 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Axiomatization of Boolean Connexive Logics with syncategorematic negation and modalities
In the article we investigate three classes of extended Boolean Connexive Logics. Two of them are extensions of Modal and non-Modal Boolean Connexive Logics with a property of closure under an arbitrary number of negations. The remaining one is an extension of Modal Boolean Connexive Logic with a property of closure under the function of demodalization. In our work we provide a formal presentation of mentioned properties and axiom schemata that allow us to incorporate them into Hilbert-style ca…

This https://arxiv.org/abs/2402.16908 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csET_…

Lightweight, error-tolerant edge detection using memristor-enabled stochastic logics
The demand for efficient edge vision has spurred the interest in developing stochastic computing approaches for performing image processing tasks. Memristors with inherent stochasticity readily introduce probability into the computations and thus enable stochastic image processing computations. Here, we present a stochastic computing approach for edge detection, a fundamental image processing technique, facilitated with memristor-enabled stochastic logics. Specifically, we integrate the memrist…

Stalnaker's Epistemic Logic in Isabelle/HOL
Laura P. Gamboa Guzman (Iowa State University, Ames, Iowa), Kristin Y. Rozier (Iowa State University, Ames, Iowa)
https://arxiv.org/abs/2404.14919

Stalnaker's Epistemic Logic in Isabelle/HOL
The foundations of formal models for epistemic and doxastic logics often rely on certain logical aspects of modal logics such as S4 and S4.2 and their semantics; however, the corresponding mathematical results are often stated in papers or books without including a detailed proof, or a reference to it, that allows the reader to convince themselves about them. We reinforce the foundations of the epistemic logic S4.2 for countably many agents by formalizing its soundness and completeness results …

A Study on Actions for Atomic Logics
Ra\"ul Espejo-Boix
https://arxiv.org/abs/2403.07948 https://arxiv.org/pdf/2403.07948…

A Study on Actions for Atomic Logics
Nowadays there is a large number of non-classical logics, each one best suited for reasoning about some issues in abstract fields, such as linguistics or epistemology, among others. Proving interesting properties for each one of them supposes a big workload for logicians and computer scientists. We want an approach into this problematic that is modular. To adress this issue, the report shows new insights in the construction of Atomic Logics introduced by Guillaume Aucher. Atomic Logics let us r…

Taming Differentiable Logics with Coq Formalisation
Reynald Affeldt, Alessandro Bruni, Ekaterina Komendantskaya, Natalia \'Slusarz, Kathrin Stark
https://arxiv.org/abs/2403.13700

Taming Differentiable Logics with Coq Formalisation
For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to translate propositional or first-order formulae into loss functions deployed for optimisation in machine learning. At the same time, recent attempts to give programming language support for verification of neural networks showed that DLs can be used to compile ve…

Obligations and permissions on selfextensional logics
Andrea De DomenicoVrije Universiteit Amsterdam, Ali FarjamiIran University of Science and Technology, Krishna ManoorkarVrije Universiteit Amsterdam, Alessandra PalmigianoVrije Universiteit Amsterdam, University of Johannesburg, Mattia PanettiereVrije Universiteit Amsterdam, Xiaolong WangVrije Universiteit Amsterdam, Shandong University

Obligations and permissions on selfextensional logics
We further develop the abstract algebraic logic approach to input/output logic initiated in \cite{wollic22}, where the family of selfextensional logics was proposed as a general background environment for input/output logics. In this paper, we introduce and discuss the generalizations of several types of permission (negative, dual negative, static, dynamic), as well as their interactions with normative systems, to various families of selfextensional logics, thereby proposing a systematic approa…

This https://arxiv.org/abs/2306.16881 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Complexity results for modal logic with recursion via translations and tableaux
This paper studies the complexity of classical modal logics and of their extension with fixed-point operators, using translations to transfer results across logics. In particular, we show several complexity results for multi-agent logics via translations to and from the $μ$-calculus and modal logic, which allow us to transfer known upper and lower bounds. We also use these translations to introduce a terminating tableau system for the logics we study, based on Kozen's tableau for the $μ$-calc…

This https://arxiv.org/abs/2403.14043 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Modal logic, fundamentally
Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal logics via algebraic representation theorems. We begin with complete lattices $L$ equipped with an antitone operation $\neg$ sending $1$ to $0$, a completely multiplicative operation $\Box$, and a completely additive operation $\Diamond$. Such lattice expansions …

This https://arxiv.org/abs/2403.00201 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Constructive S4 modal logics with the finite birelational frame property
The logics $\mathsf{CS4}$ and $\mathsf{IS4}$ are the two leading intuitionistic variants of the modal logic $\mathsf{S4}$. Whether the finite model property holds for each of these logics have been long-standing open problems. It was recently shown that $\mathsf{IS4}$ has the finite frame property and thus the finite model property. In this paper, we prove that $\mathsf{CS4}$ also enjoys the finite frame property. Additionally, we investigate the following three logics closely related to $\ma…

Modal reduction principles: a parametric shift to graphs
Willem Conradie, Krishna Manoorkar, Alessandra Palmigiano, Mattia Panettiere
https://arxiv.org/abs/2403.14026

Modal reduction principles: a parametric shift to graphs
Graph-based frames have been introduced as a logical framework which internalizes an inherent boundary to knowability. They also support the interpretation of lattice-based (modal) logics as hyper-constructive logics of evidential reasoning. Conceptually, the present paper proposes graph-based frames as a formal framework suitable for generalizing Pawlak's rough set theory to a setting in which inherent limits to knowability need to be considered. Technically, the present paper establishes syst…

Mechanised uniform interpolation for modal logics K, GL and iSL
Hugo F\'er\'ee, Iris van der Giessen, Sam van Gool, Ian Shillito
https://arxiv.org/abs/2402.10494

Mechanised uniform interpolation for modal logics K, GL and iSL
The uniform interpolation property in a given logic can be understood as the definability of propositional quantifiers. We mechanise the computation of these quantifiers and prove correctness in the Coq proof assistant for three modal logics, namely: (1) the modal logic K, for which a pen-and-paper proof exists; (2) Gödel-Löb logic GL, for which our formalisation clarifies an important point in an existing, but incomplete, sequent-style proof; and (3) intuitionistic strong Löb logic iSL, for…

This https://arxiv.org/abs/2402.03165 has been replaced.
link: https://scholar.google.com/scholar?q=a

Risk-Aware MPC for Stochastic Systems with Runtime Temporal Logics
This paper concerns the risk-aware control of stochastic systems with temporal logic specifications dynamically assigned during runtime. Conventional risk-aware control typically assumes that all specifications are predefined and remain unchanged during runtime. In this paper, we propose a novel, provably correct model predictive control scheme for linear systems with additive unbounded stochastic disturbances that dynamically evaluates the feasibility of runtime signal temporal logic specifica…

Upward L\"owenheim-Skolem-Tarski Numbers for Abstract Logics
Victoria Gitman, Jonathan Osinski
https://arxiv.org/abs/2404.12269 https://

Upward Löwenheim-Skolem-Tarski Numbers for Abstract Logics
Galeotti, Khomskii and Väänäanen recently introduced the notion of the upward Löwenheim-Skolem-Tarski number for a logic, strengthening the classical notion of a Hanf number. A cardinal $κ$ is the \emph{upward Löwenheim-Skolem-Tarski number} (ULST) of a logic $\mathcal L$ if it is the least cardinal with the property that whenever $M$ is a model of size at least $κ$ satisfying a sentence $φ$ in $\mathcal L$, then there are arbitrarily large models satisfying $φ$ and having $M$ as a sub…

This https://arxiv.org/abs/2212.03553 has been replaced.
link: https://scholar.google.com/scholar?q=a

Expressiveness of SHACL Features and Extensions for Full Equality and Disjointness Tests
SHACL is a W3C-proposed schema language for expressing structural constraints on RDF graphs. Recent work on formalizing this language has revealed a striking relationship to description logics. SHACL expressions can use three fundamental features that are not so common in description logics. These features are equality tests; disjointness tests; and closure constraints. Moreover, SHACL is peculiar in allowing only a restricted form of expressions (so-called targets) on the left-hand side of inc…

This https://arxiv.org/abs/2301.10037 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Hyper Hoare Logic: (Dis-)Proving Program Hyperproperties (extended version)
Hoare logics are proof systems that allow one to formally establish properties of computer programs. Traditional Hoare logics prove properties of individual program executions (such as functional correctness). Hoare logic has been generalized to prove also properties of multiple executions of a program (so-called hyperproperties, such as determinism or non-interference). These program logics prove the absence of (bad combinations of) executions. On the other hand, program logics similar to Hoar…

Local Intuitionistic Modal Logics and Their Calculi
Philippe Balbiani, Han Gao, \c{C}i\u{g}dem Gencer, Nicola Olivetti
https://arxiv.org/abs/2403.06772 htt…

Local Intuitionistic Modal Logics and Their Calculi
We investigate intuitionistic modal logics with locally interpreted $\square$ and $\lozenge$. The basic logic LIK is stronger than constructive modal logic WK and incomparable with intuitionistic modal logic IK. We propose an axiomatization of LIK and some of its extensions. We propose bi-nested calculi for LIK and these extensions, thus providing both a decision procedure and a procedure of finite countermodel extraction.

This https://arxiv.org/abs/2210.09095 has been replaced.
link: https://scholar.google.com/scholar?q=a

Qualitative reasoning in a two-layered framework
The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events. The paper is divided into two parts. In the first part, we formalise reasoning with the qualitative counterparts of capacities, belief functions, and probabilities, within the framework of two-layered logics. Namely, we provide two-layered logics built over the classical propositional logic using a u…

The interpolant existence problem for weak K4 and difference logic
Agi Kurucz, Frank Wolter, Michael Zakharyaschev
https://arxiv.org/abs/2403.11255 https:/…

The interpolant existence problem for weak K4 and difference logic
As well known, weak K4 and the difference logic DL do not enjoy the Craig inter- polation property. Our concern here is the problem of deciding whether any given implication does have an interpolant in these logics. We show that the nonexistence of an interpolant can always be witnessed by a pair of bisimilar models of polynomial size for DL and of triple-exponential size for weak K4, and so the interpolant existence problems for these logics are decidable in coNP and coN3ExpTime, respectively.…

This https://arxiv.org/abs/2210.09095 has been replaced.
link: https://scholar.google.com/scholar?q=a

Qualitative reasoning in a two-layered framework
The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events. The paper is divided into two parts. In the first part, we formalise reasoning with the qualitative counterparts of capacities, belief functions, and probabilities, within the framework of two-layered logics. Namely, we provide two-layered logics built over the classical propositional logic using a u…

This https://arxiv.org/abs/2308.15426 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Combining swap structures: the case of Paradefinite Ivlev-like modal logics based on FDE
The aim of this paper is to combine several Ivlev-like modal systems characterized by 4-valued non-deterministic matrices (Nmatrices) with IDM4, a 4-valued expansion of Belnap-Dunn's logic FDE with an implication introduced by Pynko in 1999. In order to do this, we introduce a new methodology for combining logics which are characterized by means of swap structures, based on what we call superposition of snapshots. In particular, the combination of IDM4 with Tm, the 4-valued Ivlev's version of K…

This https://arxiv.org/abs/2307.09913 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Exploring Non-Regular Extensions of Propositional Dynamic Logic with Description-Logics Features
We investigate the impact of non-regular path expressions on the decidability of satisfiability checking and querying in description logics extending ALC. Our primary objects of interest are ALCreg and ALCvpl, the extensions of with path expressions employing, respectively, regular and visibly-pushdown languages. The first one, ALCreg, is a notational variant of the well-known Propositional Dynamic Logic of Fischer and Ladner. The second one, ALCvpl, was introduced and investigated by Loding an…

Modal logic, fundamentally
Wesley H. Holliday
https://arxiv.org/abs/2403.14043 https://arxiv.org/pdf/2403.14043

Modal logic, fundamentally
Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal logics via algebraic representation theorems. We begin with complete lattices $L$ equipped with an antitone operation $\neg$ sending $1$ to $0$, a completely multiplicative operation $\Box$, and a completely additive operation $\Diamond$. Such lattice expansions …

Generalisation of proof simulation procedures for Frege systems by M.L.~Bonet and S.R.~Buss
Daniil Kozhemiachenko
https://arxiv.org/abs/2403.09119 https://…

Generalisation of proof simulation procedures for Frege systems by M.L.~Bonet and S.R.~Buss
In this paper, we present a~generalisation of proof simulation procedures for Frege systems by Bonet and Buss to some logics for which the deduction theorem does not hold. In particular, we study the case of finite-valued Łukasiewicz logics. To this end, we provide proof systems that augment Avron's Frege system for Łukasiewicz three-valued logic with nested and general versions of the disjunction elimination rule, respectively. For these systems we provide upper bounds on speed-ups w.r.t.\ b…

This https://arxiv.org/abs/2010.14073 has been replaced.
link: https://scholar.google.com/scholar?q=a

Structure-based Optical Logics Without Using Transistors
The commercialization of transistors capable of both switching and amplification in 1960 resulted in the development of second-generation computers, which resulted in the miniaturization and lightening while accelerating the reduction and development of production costs. However, the self-resistance and the resistance used in conjunction with semiconductors, which are the basic principles of computers, generate a lot of heat, which results in semiconductor obsolescence, and limits the computati…

This https://arxiv.org/abs/2309.06764 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Adding an Implication to Logics of Perfect Paradefinite Algebras
Perfect paradefinite algebras are De Morgan algebras expanded with an operation that allows for the full behavior of classical negation to be restored. They form a variety that is term-equivalent to the variety of involutive Stone algebras. Their associated multiple-conclusion (Set-Set) and single-conclusion (Set-Fmla) order-preserving logics are non-algebraizable self-extensional logics of formal inconsistency and undeterminedness determined by a six-valued matrix, studied in depth by Gomes et…

Generalisation of proof simulation procedures for Frege systems by M.L.~Bonet and S.R.~Buss
Daniil Kozhemiachenko
https://arxiv.org/abs/2403.09119 https://…

Generalisation of proof simulation procedures for Frege systems by M.L.~Bonet and S.R.~Buss
In this paper, we present a~generalisation of proof simulation procedures for Frege systems by Bonet and Buss to some logics for which the deduction theorem does not hold. In particular, we study the case of finite-valued Łukasiewicz logics. To this end, we provide proof systems that augment Avron's Frege system for Łukasiewicz three-valued logic with nested and general versions of the disjunction elimination rule, respectively. For these systems we provide upper bounds on speed-ups w.r.t.\ b…

Almost-Sure Termination by Guarded Refinement
Simon Oddershede Gregersen, Alejandro Aguirre, Philipp G. Haselwarter, Joseph Tassarotti, Lars Birkedal
https://arxiv.org/abs/2404.08494

Almost-Sure Termination by Guarded Refinement
Almost-sure termination is an important correctness property for probabilistic programs, and a number of program logics have been developed for establishing it. However, these logics have mostly been developed for first-order programs written in languages with specific syntactic patterns for looping. In this paper, we consider almost-sure termination for higher-order probabilistic programs with general references. This combination of features allows for recursion and looping to be encoded throu…

Logics of False Belief and Radical Ignorance
Jie Fan
https://arxiv.org/abs/2404.07442 https://arxiv.org/pdf/2404.07442

Logics of False Belief and Radical Ignorance
In the literature, the question about how to axiomatize the transitive logic of false belief is thought of as hard and left as an open problem. In this paper, among other contributions, we deal with this problem. In more details, although the standard doxastic operator is undefinable with the operator of false belief, the former is {\em almost definable} with the latter. On one hand, the involved almost definability schema guides us to find the desired core axioms for the transitive logic and t…

This https://arxiv.org/abs/2308.14581 has been replaced.
link: https://scholar.google.com/scholar?q=a

Many-valued coalgebraic logic over semi-primal varieties
We study many-valued coalgebraic logics with semi-primal algebras of truth-degrees. We provide a systematic way to lift endofunctors defined on the variety of Boolean algebras to endofunctors on the variety generated by a semi-primal algebra. We show that this can be extended to a technique to lift classical coalgebraic logics to many-valued ones, and that (one-step) completeness and expressivity are preserved under this lifting. For specific classes of endofunctors, we also describe how to obt…

Complexity of the Model Checking problem for inquisitive propositional and modal logic
Gianluca Grilletti, Ivano Ciardelli
https://arxiv.org/abs/2403.14260

Complexity of the Model Checking problem for inquisitive propositional and modal logic
The aim of this paper is to study the complexity of the model checking problem MC for inquisitive propositional logic InqB and for inquisitive modal logic InqM, that is, the problem of deciding whether a given finite structure for the logic satisfies a given formula. In recent years, this problem has been thoroughly investigated for several variations of dependence and teams logics, systems closely related to inquisitive logic. Building upon some ideas presented by Yang, we prove that the model…

This https://arxiv.org/abs/2212.03553 has been replaced.
link: https://scholar.google.com/scholar?q=a

Expressiveness of SHACL Features and Extensions for Full Equality and Disjointness Tests
SHACL is a W3C-proposed schema language for expressing structural constraints on RDF graphs. Recent work on formalizing this language has revealed a striking relationship to description logics. SHACL expressions can use three fundamental features that are not so common in description logics. These features are equality tests; disjointness tests; and closure constraints. Moreover, SHACL is peculiar in allowing only a restricted form of expressions (so-called targets) on the left-hand side of inc…

This https://arxiv.org/abs/2212.03553 has been replaced.
link: https://scholar.google.com/scholar?q=a

Expressiveness of SHACL Features and Extensions for Full Equality and Disjointness Tests
SHACL is a W3C-proposed schema language for expressing structural constraints on RDF graphs. Recent work on formalizing this language has revealed a striking relationship to description logics. SHACL expressions can use three fundamental features that are not so common in description logics. These features are equality tests; disjointness tests; and closure constraints. Moreover, SHACL is peculiar in allowing only a restricted form of expressions (so-called targets) on the left-hand side of inc…

This https://arxiv.org/abs/2307.09913 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Exploring Non-Regular Extensions of Propositional Dynamic Logic with Description-Logics Features
We investigate the impact of non-regular path expressions on the decidability of satisfiability checking and querying in description logics extending ALC. Our primary objects of interest are ALCreg and ALCvpl, the extensions of with path expressions employing, respectively, regular and visibly-pushdown languages. The first one, ALCreg, is a notational variant of the well-known Propositional Dynamic Logic of Fischer and Ladner. The second one, ALCvpl, was introduced and investigated by Loding an…

Nonclassical logics and multivariate truth values
Volodymyr M. Zhuravlov
https://arXiv.org/abs/2401.15117 https://arXiv.org/pdf/2401.…

Nonclassical logics and multivariate truth values
The article demonstrates that logic is not necessarily singleton and does not always have the standard interpretation of negation. Appropriate generalizations of logic are suggested. Positive logic and multivalued negation operations are examined. An attempt is made to abstract from the fixed and absolute values of truth and falsehood; the ambiguity of logical values is interpreted as their relativity, projective logic.

Multi-modalities and non-commutativity/associativity in functorial linear logic: a case study
Carlos Olarte, Elaine Pimentel
https://arxiv.org/abs/2404.11445

Multi-modalities and non-commutativity/associativity in functorial linear logic: a case study
Similar to modal connectives, the exponential ! in intuitionistic linear logic (ILL) is not canonical, in the sense that if $i\not= j$ then $!^i F\not\equiv !^j F$. Intuitively, this means that we can mark the exponential with labels taken from a set I organized in a pre-order $\preceq$, obtaining (possibly infinitely-many) exponentials ($!^i$ for $i\in I$). There are, however, two main differences between multi-modalities in normal modal logics and subexponentials in linear logic. i. substru…

This https://arxiv.org/abs/2305.05457 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the structure of Bochvar algebras
Bochvar algebras consist of the quasivariety BCA playing the role of equivalent algebraic semantics for Bochvar (external) logic, a logical formalism introduced by Bochvar in the realm of (weak) Kleene logics. In this paper, we provide an algebraic investigation of the structure of Bochvar algebras. In particular, we prove a representation theorem based on Plonka sums and investigate the lattice of subquasivarieties, showing that Bochvar (external) logic has only one proper extension (apart fro…

This https://arxiv.org/abs/2308.15465 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Sharing proofs with predicative theories through universe polymorphic elaboration
As the development of formal proofs is a time-consuming task, it is important to devise ways of sharing the already written proofs to prevent wasting time redoing them. One of the challenges in this domain is to translate proofs written in proof assistants based on impredicative logics to proof assistants based on predicative logics, whenever impredicativity is not used in an essential way. In this paper we present a transformation for sharing proofs with a core predicative system supporting …

Unifying Graded Linear Logic and Differential Operators
Flavien BreuvartUSPN, Marie KerjeanUSPN, CNRS, Simon MirwasserUSPN
https://arxiv.org/abs/2402.09138

Unifying Graded Linear Logic and Differential Operators
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which can describe the resource management or the complexity analysis of a program. From an other perspective, Differential Linear Logic is an extension which allows the linearization of proofs. In this article, we merge these two directions by first defining a dif…

First-Order Fischer Servi Logic
Ahmee Christensen
https://arxiv.org/abs/2402.06600 https://arxiv.org/pdf/2402.06600

First-Order Fischer Servi Logic
We prove the completeness of a first-order analogue of the Fischer Servi logic $\mathsf{FS}$ with respect to its expected birelational semantics. To this end we introduce the notion of the $\textit{trace model}$ and, much like in a canonical model argument, prove a truth lemma. We conclude by examining a number of other first-order Fischer Servi logics, including the first-order analogue of $\mathsf{FSS4}$, whose completeness can be similarly proved.

Realizability in Semantics-Guided Synthesis Done Eagerly
Roland Meyer, Jakob Tepe, Sebastian Wolff
https://arxiv.org/abs/2403.05607 https://

Realizability in Semantics-Guided Synthesis Done Eagerly
We present realizability and realization logic, two program logics that jointly address the problem of finding solutions in semantics-guided synthesis. What is new is that we proceed eagerly and not only analyze a single candidate program but a whole set. Realizability logic computes information about the set of candidate programs in a forward fashion. Realization logic uses this information as guidance to identify a suitable candidate in a backward fashion. Realizability logic is able to analy…

Weak Simplicial Bisimilarity for Polyhedral Models and SLCS_eta -- Extended Version
Nick Bezhanishvili, Vincenzo Ciancia, David Gabelaia, Mamuka Jibladze, Diego Latella, Mieke Massink, Erik P. de Vink
https://arxiv.org/abs/2404.06131

Weak Simplicial Bisimilarity for Polyhedral Models and SLCS_eta -- Extended Version
In the context of spatial logics and spatial model checking for polyhedral models - mathematical basis for visualisations in continuous space - we propose a weakening of simplicial bisimilarity. We additionally propose a corresponding weak notion of +/--bisimilarity on cell-poset models, a discrete representation of polyhedral models. We show that two points are weakly simplicial bisimilar iff their repesentations are weakly +/--bisimilar. The advantage of this weaker notion is that it leads to…

This https://arxiv.org/abs/2403.03148 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Obligations and permissions, algebraically
We further develop the algebraic approach to input/output logic initiated in \cite{wollic22}, where subordination algebras and a family of their generalizations were proposed as a semantic environment of various input/output logics.In particular, we consider precontact algebras as a suitable algebraic environment for negative permission, and we characterize properties of several types of permission (negative, static, dynamic), as well as their interactions with normative systems, by means of su…

Obligations and permissions, algebraically
Andrea De Domenico, Ali Farjami, Krishna Manoorkar, Alessandra Palmigiano, Mattia Panettiere, Xiaolong Wang
https://arxiv.org/abs/2403.03148

Obligations and permissions, algebraically
We further develop the algebraic approach to input/output logic initiated in \cite{wollic22}, where subordination algebras and a family of their generalizations were proposed as a semantic environment of various input/output logics.In particular, we consider precontact algebras as a suitable algebraic environment for negative permission, and we characterize properties of several types of permission (negative, static, dynamic), as well as their interactions with normative systems, by means of su…

This https://arxiv.org/abs/2212.11055 has been replaced.
link: https://scholar.google.com/scholar?q=a

Coalgebraic Satisfiability Checking for Arithmetic $μ$-Calculi
The coalgebraic $μ$-calculus provides a generic semantic framework for fixpoint logics over systems whose branching type goes beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. Previous work on the coalgebraic $μ$-calculus includes an exponential-time upper bound on satisfiability checking, which however relies on the availability of tableau rules for the next-step modalities that are sufficiently well-behaved in a formally defined sense; in particular, rule ma…

Simple tableaux for two expansions of G\"odel modal logic
Marta Bilkova, Thomas Ferguson, Daniil Kozhemiachenko
https://arXiv.org/abs/2401.15395 https…

Simple tableaux for two expansions of Gödel modal logic
This paper considers two logics. The first one, $\mathbf{K}\mathsf{G}_\mathsf{inv}$, is an expansion of the Gödel modal logic $\mathbf{K}\mathsf{G}$ with the involutive negation $\sim_\mathsf{i}$ defined as $v({\sim_\mathsf{i}}ϕ,w)=1-v(ϕ,w)$. The second one, $\mathbf{K}\mathsf{G}_\mathsf{bl}$, is the expansion of $\mathbf{K}\mathsf{G}_\mathsf{inv}$ with the bi-lattice connectives and modalities. We explore their semantical properties w.r.t. the standard semantics on $[0,1]$-valued Kripke fra…

This https://arxiv.org/abs/2206.13731 has been replaced.
link: https://scholar.google.com/scholar?q=a

On two-variable guarded fragment logic with expressive local Presburger constraints
We consider the extension of the two-variable guarded fragment logic with local Presburger quantifiers. These are quantifiers that can express properties such as "the number of incoming blue edges plus twice the number of outgoing red edges is at most three times the number of incoming green edges" and captures various description logics with counting, but without constant symbols. We show that the satisfiability problem for this logic is EXP-complete. While the lower bound already holds for th…

This https://arxiv.org/abs/2006.01193 has been replaced.
link: https://scholar.google.com/scholar?q=a

Two variable logic with ultimately periodic counting
We consider the extension of two variable logic with quantifiers that state that the number of elements where a formula holds should belong to a given ultimately periodic set. We show that both satisfiability and finite satisfiability of the logic are decidable. We also show that the spectrum of any sentence is definable in Presburger arithmetic. In the process we present several refinements to the ``biregular graph method''. In this method, decidability issues concerning two-variable logics ar…

Interpolant Existence is Undecidable for Two-Variable First-Order Logic with Two Equivalence Relations
Frank Wolter, Michael Zakharyaschev
https://arxiv.org/abs/2404.02683

Interpolant Existence is Undecidable for Two-Variable First-Order Logic with Two Equivalence Relations
The interpolant existence problem (IEP) for a logic L is to decide, given formulas P and Q, whether there exists a formula I, built from the shared symbols of P and Q, such that P entails I and I entails Q in L. If L enjoys the Craig interpolation property (CIP), then the IEP reduces to validity in L. Recently, the IEP has been studied for logics without the CIP. The results obtained so far indicate that even though the IEP can be computationally harder than validity, it is decidable when L is …

This https://arxiv.org/abs/2403.14260 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Complexity of the Model Checking problem for inquisitive propositional and modal logic
The aim of this paper is to study the complexity of the model checking problem MC for inquisitive propositional logic InqB and for inquisitive modal logic InqM, that is, the problem of deciding whether a given finite structure for the logic satisfies a given formula. In recent years, this problem has been thoroughly investigated for several variations of dependence and teams logics, systems closely related to inquisitive logic. Building upon some ideas presented by Yang, we prove that the model…

This https://arxiv.org/abs/2403.14260 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Complexity of the Model Checking problem for inquisitive propositional and modal logic
The aim of this paper is to study the complexity of the model checking problem MC for inquisitive propositional logic InqB and for inquisitive modal logic InqM, that is, the problem of deciding whether a given finite structure for the logic satisfies a given formula. In recent years, this problem has been thoroughly investigated for several variations of dependence and teams logics, systems closely related to inquisitive logic. Building upon some ideas presented by Yang, we prove that the model…