Tootfinder

Counting Like Transformers: Compiling Temporal Counting Logic Into Softmax Transformers
Andy Yang, David Chiang
https://arxiv.org/abs/2404.04393 https://…

Counting Like Transformers: Compiling Temporal Counting Logic Into Softmax Transformers
Deriving formal bounds on the expressivity of transformers, as well as studying transformers that are constructed to implement known algorithms, are both effective methods for better understanding the computational power of transformers. Towards both ends, we introduce the temporal counting logic $\textbf{K}_\text{t}$[#] alongside the RASP variant $\textbf{C-RASP}$. We show they are equivalent to each other, and that together they are the best-known lower bound on the formal expressivity of fut…

This https://arxiv.org/abs/2306.04089 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Fully Automated Verification of Linear Time-Invariant Systems against Signal Temporal Logic Specifications via Reachability Analysis
While reachability analysis is one of the most promising approaches for formal verification of dynamic systems, a major disadvantage preventing a more widespread application is the requirement to manually tune algorithm parameters such as the time step size. Manual tuning is especially problematic if one aims to verify that the system satisfies complicated specifications described by signal temporal logic formulas since the effect the tightness of the reachable set has on the satisfaction of th…

This https://arxiv.org/abs/2404.10362 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSE_…

3DGen: AI-Assisted Generation of Provably Correct Binary Format Parsers
Improper parsing of attacker-controlled input is a leading source of software security vulnerabilities, especially when programmers transcribe informal format descriptions in RFCs into efficient parsing logic in low-level, memory unsafe languages. Several researchers have proposed formal specification languages for data formats from which efficient code can be extracted. However, distilling informal requirements into formal specifications is challenging and, despite their benefits, new, formal …

This https://arxiv.org/abs/2401.01884 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

A rewriting-logic-with-SMT-based formal analysis and parameter synthesis framework for parametric time Petri nets
This paper presents a concrete and a symbolic rewriting logic semantics for parametric time Petri nets with inhibitor arcs (PITPNs), a flexible model of timed systems where parameters are allowed in firing bounds. We prove that our semantics is bisimilar to the "standard" semantics of PITPNs. This allows us to use the rewriting logic tool Maude, combined with SMT solving, to provide sound and complete formal analyses for PITPNs. We develop and implement a new general folding approach for symbol…

This https://arxiv.org/abs/2310.00163 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

Cook2LTL: Translating Cooking Recipes to LTL Formulae using Large Language Models
Cooking recipes are challenging to translate to robot plans as they feature rich linguistic complexity, temporally-extended interconnected tasks, and an almost infinite space of possible actions. Our key insight is that combining a source of cooking domain knowledge with a formalism that captures the temporal richness of cooking recipes could enable the extraction of unambiguous, robot-executable plans. In this work, we use Linear Temporal Logic (LTL) as a formal language expressive enough to m…

Automated Control Logic Test Case Generation using Large Language Models
Heiko Koziolek, Virendra Ashiwal, Soumyadip Bandyopadhyay, Chandrika K R
https://arxiv.org/abs/2405.01874 …

Automated Control Logic Test Case Generation using Large Language Models
Testing PLC and DCS control logic in industrial automation is laborious and challenging since appropriate test cases are often complex and difficult to formulate. Researchers have previously proposed several automated test case generation approaches for PLC software applying symbolic execution and search-based techniques. Often requiring formal specifications and performing a mechanical analysis of programs, these approaches may uncover specific programming errors but sometimes suffer from stat…

This https://arxiv.org/abs/2401.01668 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Combinatory Intensional Logic: Formal foundations
Combinatory Intensional Logic (CIL) is a general framework for a formal theory of natural language meaning and reasoning, including intensional logic. What sets this approach apart is a syntax close to the logico-semantic mechanisms of natural language and being compatible with logical realism, the view that properties, relations and propositions are entities in their own right as well as furnishing the senses of linguistic expressions. CIL models, which formalize a realm of interweavings of …

This https://arxiv.org/abs/2310.00163 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

Cook2LTL: Translating Cooking Recipes to LTL Formulae using Large Language Models
Cooking recipes are challenging to translate to robot plans as they feature rich linguistic complexity, temporally-extended interconnected tasks, and an almost infinite space of possible actions. Our key insight is that combining a source of cooking domain knowledge with a formalism that captures the temporal richness of cooking recipes could enable the extraction of unambiguous, robot-executable plans. In this work, we use Linear Temporal Logic (LTL) as a formal language expressive enough to m…

This https://arxiv.org/abs/2212.06937 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the $\infty$-topos semantics of homotopy type theory
Many introductions to homotopy type theory and the univalence axiom gloss over the semantics of this new formal system in traditional set-based foundations. This expository article, written as lecture notes to accompany a 3-part mini course delivered at the Logic and Higher Structures workshop at CIRM-Luminy, attempts to survey the state of the art, first presenting Voevodsky's simplicial model of univalent foundations and then touring Shulman's vast generalization, which provides an interpreta…

This https://arxiv.org/abs/2402.14798 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCL_…

Enhancing Systematic Decompositional Natural Language Inference Using Informal Logic
Contemporary language models enable new opportunities for structured reasoning with text, such as the construction and evaluation of intuitive, proof-like textual entailment trees without relying on brittle formal logic. However, progress in this direction has been hampered by a long-standing lack of a clear protocol for determining what valid compositional entailment is. This absence causes noisy datasets and limited performance gains by modern neuro-symbolic engines. To address these problems…

@… @… I won't be attending, but am very curious about the topic. I recently spoke with someone from Princeton working on the topic. Was very disappointed to find out it all boils down to computation and formal logic to them. I disagr…

This https://arxiv.org/abs/2108.12003 has been replaced.
link: https://scholar.google.com/scholar?q=a

Automata Linear Dynamic Logic on Finite Traces
Temporal logics are widely used by the Formal Methods and AI communities. Linear Temporal Logic is a popular temporal logic and is valued for its ease of use as well as its balance between expressiveness and complexity. LTL is equivalent in expressiveness to Monadic First-Order Logic and satisfiability for LTL is PSPACE-complete. Linear Dynamic Logic (LDL), another temporal logic, is equivalent to Monadic Second-Order Logic, but its method of satisfiability checking cannot be applied to a nontr…

AlloyInEcore: Embedding of First-Order Relational Logic into Meta-Object Facility for Automated Model Reasoning
Ferhat Erata, Arda Goknil, Ivan Kurtev, Bedir Tekinerdogan
https://arxiv.org/abs/2403.02652

AlloyInEcore: Embedding of First-Order Relational Logic into Meta-Object Facility for Automated Model Reasoning
We present AlloyInEcore, a tool for specifying metamodels with their static semantics to facilitate automated, formal reasoning on models. Software development projects require that software systems be specified in various models (e.g., requirements models, architecture models, test models, and source code). It is crucial to reason about those models to ensure the correct and complete system specifications. AlloyInEcore allows the user to specify metamodels with their static semantics, while, u…

This https://arxiv.org/abs/2307.09561 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Non-distributive description logic
We define LE-ALC, a generalization of the description logic ALC based on the propositional logic of general (i.e. not necessarily distributive) lattices, and semantically interpreted on relational structures based on formal contexts from Formal Concept Analysis (FCA). The description logic LE-ALC allows us to formally describe databases with objects, features, and formal concepts, represented according to FCA as Galois-stable sets of objects and features. We describe ABoxes and TBoxes in LE-ALC…

Reactive Temporal Logic-based Planning and Control for Interactive Robotic Tasks
Farhad Nawaz, Shaoting Peng, Lars Lindemann, Nadia Figueroa, Nikolai Matni
https://arxiv.org/abs/2404.19594

Reactive Temporal Logic-based Planning and Control for Interactive Robotic Tasks
Robots interacting with humans must be safe, reactive and adapt online to unforeseen environmental and task changes. Achieving these requirements concurrently is a challenge as interactive planners lack formal safety guarantees, while safe motion planners lack flexibility to adapt. To tackle this, we propose a modular control architecture that generates both safe and reactive motion plans for human-robot interaction by integrating temporal logic-based discrete task level plans with continuous D…

Enhancing Systematic Decompositional Natural Language Inference Using Informal Logic
Nathaniel Weir, Kate Sanders, Orion Weller, Shreya Sharma, Dongwei Jiang, Zhengping Zhang, Bhavana Dalvi Mishra, Oyvind Tafjord, Peter Jansen, Peter Clark, Benjamin Van Durme
https://arxiv.org/abs/2402.14798…

Enhancing Systematic Decompositional Natural Language Inference Using Informal Logic
Contemporary language models enable new opportunities for structured reasoning with text, such as the construction and evaluation of intuitive, proof-like textual entailment trees without relying on brittle formal logic. However, progress in this direction has been hampered by a long-standing lack of a clear protocol for determining what valid compositional entailment is. This absence causes noisy datasets and limited performance gains by modern neuro-symbolic engines. To address these problems…

PECR: A formal system based on computability logic
G. Pantelis
https://arxiv.org/abs/2403.14880 https://arxiv.org/pdf/2403.14880

PECR: A formal system based on computability logic
PECR is a formal system designed to explore the properties of computability of programs on a real-world computer. As such PECR incorporates the finite resources of the machine upon which a program is to be executed. The main features of the formal system will be presented and its practical applications will be discussed. Of particular interest is the implementation of the formal system to the exploration of the laws of nature that lead to rigorous constructions of computer models of real-world …

Formal Verification of Unknown Stochastic Systems via Non-parametric Estimation
Zhi Zhang, Chenyu Ma, Saleh Soudijani, Sadegh Soudjani
https://arxiv.org/abs/2403.05350

Formal Verification of Unknown Stochastic Systems via Non-parametric Estimation
A novel data-driven method for formal verification is proposed to study complex systems operating in safety-critical domains. The proposed approach is able to formally verify discrete-time stochastic dynamical systems against temporal logic specifications only using observation samples and without the knowledge of the model, and provide a probabilistic guarantee on the satisfaction of the specification. We first propose the theoretical results for using non-parametric estimation to estimate an …

This https://arxiv.org/abs/2307.09561 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Non-distributive description logic
We define LE-ALC, a generalization of the description logic ALC based on the propositional logic of general (i.e. not necessarily distributive) lattices, and semantically interpreted on relational structures based on formal contexts from Formal Concept Analysis (FCA). The description logic LE-ALC allows us to formally describe databases with objects, features, and formal concepts, represented according to FCA as Galois-stable sets of objects and features. We describe ABoxes and TBoxes in LE-ALC…

Reasoning About Group Polarization: From Semantic Games to Sequent Systems
Robert Freiman, Carlos Olarte, Elaine Pimentel, Christian G. Ferm\"uller
https://arxiv.org/abs/2405.01322

Reasoning About Group Polarization: From Semantic Games to Sequent Systems
Group polarization, the phenomenon where individuals become more extreme after interacting, has been gaining attention, especially with the rise of social media shaping people's opinions. Recent interest has emerged in formal reasoning about group polarization using logical systems. In this work we consider the modal logic PNL that captures the notion of agents agreeing or disagreeing on a given topic. Our contribution involves enhancing PNL with advanced formal reasoning techniques, instead of…

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…

Logic in Mathematics and Computer Science
Richard Zach
https://arxiv.org/abs/2404.09033 https://arxiv.org/pdf/2404.09033

Logic in Mathematics and Computer Science
Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert's consistency program. Si…

Embedding Differential Dynamic Logic in PVS
J. Tanner Slagel (NASA), Mariano Moscato (NIA), Lauren White (NASA), C\'esar A. Mu\~noz (NASA), Swee Balachandran (NIA), Aaron Dutle (NASA)
https://arxiv.org/abs/2404.15214

Embedding Differential Dynamic Logic in PVS
Differential dynamic logic (dL) is a formal framework for specifying and reasoning about hybrid systems, i.e., dynamical systems that exhibit both continuous and discrete behaviors. These kinds of systems arise in many safety- and mission-critical applications. This paper presents a formalization of dL in the Prototype Verification System (PVS) that includes the semantics of hybrid programs and dL's proof calculus. The formalization embeds dL into the PVS logic, resulting in a version of dL wh…

This https://arxiv.org/abs/2404.09033 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Logic in Mathematics and Computer Science
Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert's consistency program. Si…

Reconciling Conflicting Data Curation Actions: Transparency Through Argumentation
Yilin Xia, Shawn Bowers, Lan Li, Bertram Lud\"ascher
https://arxiv.org/abs/2403.08257

Reconciling Conflicting Data Curation Actions: Transparency Through Argumentation
We propose a new approach for modeling and reconciling conflicting data cleaning actions. Such conflicts arise naturally in collaborative data curation settings where multiple experts work independently and then aim to put their efforts together to improve and accelerate data cleaning. The key idea of our approach is to model conflicting updates as a formal \emph{argumentation framework}(AF). Such argumentation frameworks can be automatically analyzed and solved by translating them to a logic p…

This https://arxiv.org/abs/2401.14516 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Beyond the Spell: A Dynamic Logic Analysis of Misdirection
Misdirection can be defined as the intentional action of causing some misrepresentation in an agent, or in a group of agents. Those misrepresentations may result from verbal actions, as in linguistic deception, or from visual actions, as in visual misdirection. Examples of visual misdirection abound (e.g. in nature, in the military), with magic tricks providing a vivid illustration. So far, various types of verbal misdirection have been investigated from a formal perspective (e.g. lying, bluffi…

Scaling Learning based Policy Optimization for Temporal Tasks via Dropout
Navid Hashemi, Bardh Hoxha, Danil Prokhorov, Georgios Fainekos, Jyotirmoy Deshmukh
https://arxiv.org/abs/2403.15826

Scaling Learning based Policy Optimization for Temporal Tasks via Dropout
This paper introduces a model-based approach for training feedback controllers for an autonomous agent operating in a highly nonlinear environment. We desire the trained policy to ensure that the agent satisfies specific task objectives, expressed in discrete-time Signal Temporal Logic (DT-STL). One advantage for reformulation of a task via formal frameworks, like DT-STL, is that it permits quantitative satisfaction semantics. In other words, given a trajectory and a DT-STL formula, we can comp…

3DGen: AI-Assisted Generation of Provably Correct Binary Format Parsers
Sarah Fakhoury, Markus Kuppe, Shuvendu K. Lahiri, Tahina Ramananandro, Nikhil Swamy
https://arxiv.org/abs/2404.10362

3DGen: AI-Assisted Generation of Provably Correct Binary Format Parsers
Improper parsing of attacker-controlled input is a leading source of software security vulnerabilities, especially when programmers transcribe informal format descriptions in RFCs into efficient parsing logic in low-level, memory unsafe languages. Several researchers have proposed formal specification languages for data formats from which efficient code can be extracted. However, distilling informal requirements into formal specifications is challenging and, despite their benefits, new, formal …

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 …

Sound and Complete Witnesses for Template-based Verification of LTL Properties on Polynomial Programs
Krishnendu Chatterjee, Amir Kafshdar Goharshady, Ehsan Kafshdar Goharshady, Mehrdad Karrabi, {\DH}or{\dh}E \v{Z}ikeli\'c
https://arxiv.org/abs/2403.05386

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…

3DGen: AI-Assisted Generation of Provably Correct Binary Format Parsers
Sarah Fakhoury, Markus Kuppe, Shuvendu K. Lahiri, Tahina Ramananandro, Nikhil Swamy
https://arxiv.org/abs/2404.10362

3DGen: AI-Assisted Generation of Provably Correct Binary Format Parsers
Improper parsing of attacker-controlled input is a leading source of software security vulnerabilities, especially when programmers transcribe informal format descriptions in RFCs into efficient parsing logic in low-level, memory unsafe languages. Several researchers have proposed formal specification languages for data formats from which efficient code can be extracted. However, distilling informal requirements into formal specifications is challenging and, despite their benefits, new, formal …

This https://arxiv.org/abs/2302.06164 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Logic for Veracity
This paper shows the initial stages of development, from first principles, of a formal logic to characterise and then explore issues in a broadly defined idea of Veracity, which includes properties of demonstrability, truth, trust and authenticity.

Canonical Decision Diagrams Modulo Theories
Massimo Michelutti, Gabriele Masina, Giuseppe Spallitta, Roberto Sebastiani
https://arxiv.org/abs/2404.16455 ht…

Canonical Decision Diagrams Modulo Theories
Decision diagrams (DDs) are powerful tools to represent effectively propositional formulas, which are largely used in many domains, in particular in formal verification and in knowledge compilation. Some forms of DDs (e.g., OBDDs, SDDs) are canonical, that is, (under given conditions on the atom list) they univocally represent equivalence classes of formulas. Given the limited expressiveness of propositional logic, a few attempts to leverage DDs to SMT level have been presented in the literatur…

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…

Unified Opinion Dynamic Modeling as Concurrent Set Relations in Rewriting Logic
Carlos Olarte, Carlos Ram\'irez, Camilo Rocha, Frank Valencia
https://arxiv.org/abs/2402.09021 …

Unified Opinion Dynamic Modeling as Concurrent Set Relations in Rewriting Logic
Social media platforms have played a key role in weaponizing the polarization of social, political, and democratic processes. This is, mainly, because they are a medium for opinion formation. Opinion dynamic models are a tool for understanding the role of specific social factors on the acceptance/rejection of opinions because they can be used to analyze certain assumptions on human behaviors. This work presents a framework that uses concurrent set relations as the formal basis to specify, simul…

AI-Driven Statutory Reasoning via Software Engineering Methods
Rohan Padhye
https://arxiv.org/abs/2404.09868 https://arxiv.org/pdf/24…

AI-Driven Statutory Reasoning via Software Engineering Methods
The recent proliferation of generative artificial intelligence (GenAI) technologies such as pre-trained large language models (LLMs) has opened up new frontiers in computational law. An exciting area of development is the use of AI to automate the rule-based reasoning inherent in statutory and contract law. While this form of reasoning has long been studied using classical techniques of natural language processing (NLP) and formal logic, recent solutions increasingly make use of LLMs; though th…

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…

An Encoding for CLP Problems in SMT-LIB
Daneshvar Amrollahi, Hossein Hojjat, Philipp R\"ummer
https://arxiv.org/abs/2404.14924 https://

An Encoding for CLP Problems in SMT-LIB
The input language for today's CHC solvers are commonly the standard SMT-LIB format, borrowed from SMT solvers, and the Prolog format that stems from Constraint-Logic Programming (CLP). This paper presents a new front-end of the Eldarica CHC solver that allows inputs in the Prolog language. We give a formal translation of a subset of Prolog into the SMT-LIB commands. Our initial experiments show the effectiveness of the approach and the potential benefits to both the CHC solving and CLP communi…

This https://arxiv.org/abs/2403.00934 has been replaced.
link: https://scholar.google.com/scholar?q=a

Semi-Automated Modular Formal Verification of Critical Software: Liveness and Completeness Thresholds
In this dissertation we describe two contributions to the state of the art in reasoning about liveness and safety, respectively. Programs for multiprocessor machines commonly perform busy waiting for synchronization. We propose the first separation logic for modularly verifying termination of such programs under fair scheduling. Our logic requires the proof author to associate a ghost signal with each busy-waiting loop and allows such loops to iterate while their corresponding signal $s$ is n…

This https://arxiv.org/abs/2310.19806 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Automated Verification of Equivalence Properties in Advanced Logic Programs -- Bachelor Thesis
With the increase in industrial applications using Answer Set Programming, the need for formal verification tools, particularly for critical applications, has also increased. During the program optimisation process, it would be desirable to have a tool which can automatically verify whether an optimised subprogram can replace the original subprogram. Formally this corresponds to the problem of verifying the strong equivalence of two programs. In order to do so, the translation tool anthem was d…