Tootfinder

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…

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.

This https://arxiv.org/abs/2403.05386 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csPL_…

Sound and Complete Witnesses for Template-based Verification of LTL Properties on Polynomial Programs
We study the classical problem of verifying programs with respect to formal specifications given in the linear temporal logic (LTL). We first present novel \emph{sound and complete} witnesses for LTL verification over imperative programs. Our witnesses are applicable to both universal (all runs) and existential (some run) settings. We then consider LTL formulas in which atomic propositions can be polynomial constraints and turn our focus to polynomial arithmetic programs, i.e. programs in which…

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.

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…

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…

This https://arxiv.org/abs/2304.15000 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csPL_…

Quantum Control Machine: The Limits of Control Flow in Quantum Programming
Quantum algorithms for tasks such as factorization, search, and simulation rely on control flow such as branching and iteration that depends on the value of data in superposition. High-level programming abstractions for control flow, such as switches, loops, and higher-order functions, are ubiquitous in classical languages. By contrast, many quantum languages do not provide high-level abstractions for control flow in superposition, and instead require the use of hardware-level logic gates to im…

This https://arxiv.org/abs/2210.05344 has been replaced.
link: https://scholar.google.com/scholar?q=a

From Basic Proof-theoretic Validity to Base-extension Semantics for Intuitionistic Propositional Logic
Proof-theoretic semantics (P-tS) is the approach to meaning in logic based on proof (as opposed to truth). There are two major approaches to P-tS: proof-theor\-etic validity (P-tV) and base-extension semantics (B-eS). The former is a semantics of arguments, and the latter is a semantics of logical constants. This paper demonstrates that the B-eS for intuitionistic propositional logic (IPL) encapsulates the declarative content of a basic version of P-tV. Such relationships have been considered b…

This https://arxiv.org/abs/2306.03045 has been replaced.
link: https://scholar.google.com/scholar?q=a

Designing Equilibria in Concurrent Games with Social Welfare and Temporal Logic Constraints
In game theory, mechanism design is concerned with the design of incentives so that a desired outcome of the game can be achieved. In this paper, we explore the concept of equilibrium design, where incentives are designed to obtain a desirable equilibrium that satisfies a specific temporal logic property. Our study is based on a framework where system specifications are represented as temporal logic formulae, games as quantitative concurrent game structures, and players' goals as mean-payoff ob…

This https://arxiv.org/abs/2103.02343 has been replaced.
link: https://scholar.google.com/scholar?q=a

Provability in BI's Sequent Calculus is Decidable
Warning: This paper contains a mistake, rendering the proof of the main theorem invalid. The logic of Bunched Implications (BI) combines both additive and multiplicative connectives, which include two primitive intuitionistic implications. As a consequence, contexts in the sequent presentation are not lists, nor multisets, but rather tree-like structures called bunches. This additional complexity notwithstanding, the logic has a well-behaved metatheory admitting all the familiar forms of semant…