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SAT Meets Tableaux for Linear Temporal Logic Satisfiability J. Autom. Reason. (IF 1.1) Pub Date : 2024-03-15 Luca Geatti, Nicola Gigante, Angelo Montanari, Gabriele Venturato
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Should Decisions in QCDCL Follow Prefix Order? J. Autom. Reason. (IF 1.1) Pub Date : 2024-02-09
Abstract Quantified conflict-driven clause learning (QCDCL) is one of the main solving approaches for quantified Boolean formulas (QBF). One of the differences between QCDCL and propositional CDCL is that QCDCL typically follows the prefix order of the QBF for making decisions. We investigate an alternative model for QCDCL solving where decisions can be made in arbitrary order. The resulting system
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Non-termination in Term Rewriting and Logic Programming J. Autom. Reason. (IF 1.1) Pub Date : 2024-02-02 Étienne Payet
In this paper, we define two particular forms of non-termination, namely loops and binary chains, in an abstract framework that encompasses term rewriting and logic programming. The definition of loops relies on the notion of compatibility of binary relations. We also present a syntactic criterion for the detection of a special case of binary chains. Moreover, we describe our implementation NTI and
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A Matroid-Based Automatic Prover and Coq Proof Generator for Projective Incidence Geometry J. Autom. Reason. (IF 1.1) Pub Date : 2024-01-18
Abstract We present an automatic theorem prover for projective incidence geometry. This prover does not consider coordinates. Instead, it follows a combinatorial approach based on the concept of rank. This allows to deal only with sets of points and to capture relations between objects of the projective space (equality, collinearity, coplanarity, etc.) in a homogenous way. Taking advantage of the computational
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A Formalization of the CHSH Inequality and Tsirelson’s Upper-bound in Isabelle/HOL J. Autom. Reason. (IF 1.1) Pub Date : 2023-12-19 Mnacho Echenim, Mehdi Mhalla
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Formally-Verified Round-Off Error Analysis of Runge–Kutta Methods J. Autom. Reason. (IF 1.1) Pub Date : 2023-12-06 Florian Faissole
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Formal Verification of Termination Criteria for First-Order Recursive Functions J. Autom. Reason. (IF 1.1) Pub Date : 2023-11-29 Cesar A. Muñoz, Mauricio Ayala-Rincón, Mariano M. Moscato, Aaron M. Dutle, Anthony J. Narkawicz, Ariane Alves Almeida, Andréia B. Avelar da Silva, Thiago M. Ferreira Ramos
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Saturation-Based Boolean Conjunctive Query Answering and Rewriting for the Guarded Quantification Fragments J. Autom. Reason. (IF 1.1) Pub Date : 2023-11-23 Sen Zheng, Renate A. Schmidt
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Self-evident Automated Geometric Theorem Proving Based on Complex Number Identity J. Autom. Reason. (IF 1.1) Pub Date : 2023-11-20 Xicheng Peng, Jingzhong Zhang, Mao Chen, Sannyuya Liu
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Bisequent Calculus for Four-Valued Quasi-Relevant Logics: Cut Elimination and Interpolation J. Autom. Reason. (IF 1.1) Pub Date : 2023-11-16 Andrzej Indrzejczak
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Finitary Type Theories With and Without Contexts J. Autom. Reason. (IF 1.1) Pub Date : 2023-10-07 Philipp G. Haselwarter, Andrej Bauer
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Lower Bounds for QCDCL via Formula Gauge J. Autom. Reason. (IF 1.1) Pub Date : 2023-09-27 Benjamin Böhm, Olaf Beyersdorff
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Combining Stable Infiniteness and (Strong) Politeness J. Autom. Reason. (IF 1.1) Pub Date : 2023-09-27 Ying Sheng, Yoni Zohar, Christophe Ringeissen, Andrew Reynolds, Clark Barrett, Cesare Tinelli
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Enabling Floating-Point Arithmetic in the Coq Proof Assistant J. Autom. Reason. (IF 1.1) Pub Date : 2023-09-16 Érik Martin-Dorel, Guillaume Melquiond, Pierre Roux
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Reasoning About Vectors: Satisfiability Modulo a Theory of Sequences J. Autom. Reason. (IF 1.1) Pub Date : 2023-09-15 Ying Sheng, Andres Nötzli, Andrew Reynolds, Yoni Zohar, David Dill, Wolfgang Grieskamp, Junkil Park, Shaz Qadeer, Clark Barrett, Cesare Tinelli
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Preprocessing of Propagation Redundant Clauses J. Autom. Reason. (IF 1.1) Pub Date : 2023-09-14 Joseph E. Reeves, Marijn J. H. Heule, Randal E. Bryant
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A Proof Procedure for Separation Logic with Inductive Definitions and Data J. Autom. Reason. (IF 1.1) Pub Date : 2023-09-09 Mnacho Echenim, Nicolas Peltier
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Mechanising Gödel–Löb Provability Logic in HOL Light J. Autom. Reason. (IF 1.1) Pub Date : 2023-08-29 Marco Maggesi, Cosimo Perini Brogi
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Measure Construction by Extension in Dependent Type Theory with Application to Integration J. Autom. Reason. (IF 1.1) Pub Date : 2023-08-18 Reynald Affeldt, Cyril Cohen
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Cyclic Hypersequent System for Transitive Closure Logic J. Autom. Reason. (IF 1.1) Pub Date : 2023-08-16 Anupam Das, Marianna Girlando
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A Resolution Proof System for Dependency Stochastic Boolean Satisfiability J. Autom. Reason. (IF 1.1) Pub Date : 2023-08-03 Yun-Rong Luo, Che Cheng, Jie-Hong R. Jiang
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Binary Codes that do not Preserve Primitivity J. Autom. Reason. (IF 1.1) Pub Date : 2023-07-18 Štěpán Holub, Martin Raška, Štěpán Starosta
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POSIX Lexing with Derivatives of Regular Expressions J. Autom. Reason. (IF 1.1) Pub Date : 2023-07-08 Christian Urban
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Rensets and Renaming-Based Recursion for Syntax with Bindings Extended Version J. Autom. Reason. (IF 1.1) Pub Date : 2023-07-05 Andrei Popescu
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SCL(EQ): SCL for First-Order Logic with Equality J. Autom. Reason. (IF 1.1) Pub Date : 2023-06-30 Hendrik Leidinger, Christoph Weidenbach
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A Formal Theory of Choreographic Programming J. Autom. Reason. (IF 1.1) Pub Date : 2023-05-27 Luís Cruz-Filipe, Fabrizio Montesi, Marco Peressotti
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Combining Higher-Order Logic with Set Theory Formalizations J. Autom. Reason. (IF 1.1) Pub Date : 2023-05-25 Cezary Kaliszyk, Karol Pąk
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Synthesising Programs with Non-trivial Constants J. Autom. Reason. (IF 1.1) Pub Date : 2023-05-13 Alessandro Abate, Haniel Barbosa, Clark Barrett, Cristina David, Pascal Kesseli, Daniel Kroening, Elizabeth Polgreen, Andrew Reynolds, Cesare Tinelli
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An Automatically Verified Prototype of the Android Permissions System J. Autom. Reason. (IF 1.1) Pub Date : 2023-05-12 Maximiliano Cristiá, Guido De Luca, Carlos Luna
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Unifying Splitting J. Autom. Reason. (IF 1.1) Pub Date : 2023-04-28 Gabriel Ebner, Jasmin Blanchette, Sophie Tourret
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An Automated Approach to the Collatz Conjecture J. Autom. Reason. (IF 1.1) Pub Date : 2023-04-25 Emre Yolcu, Scott Aaronson, Marijn J. H. Heule
We explore the Collatz conjecture and its variants through the lens of termination of string rewriting. We construct a rewriting system that simulates the iterated application of the Collatz function on strings corresponding to mixed binary–ternary representations of positive integers. We prove that the termination of this rewriting system is equivalent to the Collatz conjecture. We also prove that
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First-Order Theory of Rewriting for Linear Variable-Separated Rewrite Systems: Automation, Formalization, Certification J. Autom. Reason. (IF 1.1) Pub Date : 2023-04-06 Aart Middeldorp, Alexander Lochmann, Fabian Mitterwallner
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Synthetic Undecidability and Incompleteness of First-Order Axiom Systems in Coq J. Autom. Reason. (IF 1.1) Pub Date : 2023-03-12 Dominik Kirst, Marc Hermes
We mechanise the undecidability of various first-order axiom systems in Coq, employing the synthetic approach to computability underlying the growing Coq Library of Undecidability Proofs. Concretely, we cover both semantic and deductive entailment in fragments of Peano arithmetic (PA) as well as ZF and related finitary set theories, with their undecidability established by many-one reductions from
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Computer-Aided Constructions of Commafree Codes J. Autom. Reason. (IF 1.1) Pub Date : 2023-02-17 Aaron A. Windsor
We determine the maximum size \(W_k(n)\) of a commafree code with codeword length k and alphabet size n for a few previously unknown values of k and n. With the aid of modern SAT solver tooling we prove that \(W_4(5) = 139\), \(W_6(3) = 113\), and \(W_{12}(2) = 334\) and exhibit codes that achieve these bounds.
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Finding Normal Binary Floating-Point Factors Efficiently J. Autom. Reason. (IF 1.1) Pub Date : 2023-02-06 Mak Andrlon
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Superposition for Higher-Order Logic J. Autom. Reason. (IF 1.1) Pub Date : 2023-01-21 Alexander Bentkamp, Jasmin Blanchette, Sophie Tourret, Petar Vukmirović
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Efficient Extensional Binary Tries J. Autom. Reason. (IF 1.1) Pub Date : 2023-01-12 Andrew W. Appel, Xavier Leroy
Lookup tables (finite maps) are a ubiquitous data structure. In pure functional languages they are best represented using trees instead of hash tables. In pure functional languages within constructive logic, without a primitive integer type, they are well represented using binary tries instead of search trees. In this work, we introduce canonical binary tries, an improved binary-trie data structure
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Optimal Deterministic Controller Synthesis from Steady-State Distributions J. Autom. Reason. (IF 1.1) Pub Date : 2023-01-12 Alvaro Velasquez, Ismail Alkhouri, K. Subramani, Piotr Wojciechowski, George Atia
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Semantically-Guided Goal-Sensitive Reasoning: Decision Procedures and the Koala Prover J. Autom. Reason. (IF 1.1) Pub Date : 2023-01-11 Maria Paola Bonacina, Sarah Winkler
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Measuring the Readability of Geometric Proofs: The Area Method Case J. Autom. Reason. (IF 1.1) Pub Date : 2023-01-10 Pedro Quaresma, Pierluigi Graziani
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A Solver for Arrays with Concatenation J. Autom. Reason. (IF 1.1) Pub Date : 2023-01-07 Qinshi Wang, Andrew W. Appel
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Linear Depth Deduction with Subformula Property for Intuitionistic Epistemic Logic J. Autom. Reason. (IF 1.1) Pub Date : 2022-12-30 Guido Fiorino
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Formalising Szemerédi’s Regularity Lemma and Roth’s Theorem on Arithmetic Progressions in Isabelle/HOL J. Autom. Reason. (IF 1.1) Pub Date : 2022-12-19 Chelsea Edmonds, Angeliki Koutsoukou-Argyraki, Lawrence C. Paulson
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A Formalization and Proof Checker for Isabelle’s Metalogic J. Autom. Reason. (IF 1.1) Pub Date : 2022-12-12 Simon Roßkopf, Tobias Nipkow
Isabelle is a generic theorem prover with a fragment of higher-order logic as a metalogic for defining object logics. Isabelle also provides proof terms. We formalize this metalogic and the language of proof terms in Isabelle/HOL, define an executable (but inefficient) proof term checker and prove its correctness w.r.t. the metalogic. We integrate the proof checker with Isabelle and run it on a range
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Towards Formalising Schutz’ Axioms for Minkowski Spacetime in Isabelle/HOL J. Autom. Reason. (IF 1.1) Pub Date : 2022-10-01 Richard Schmoetten, Jake E. Palmer, Jacques D. Fleuriot
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Pardinus: A Temporal Relational Model Finder J. Autom. Reason. (IF 1.1) Pub Date : 2022-09-12 Nuno Macedo, Julien Brunel, David Chemouil, Alcino Cunha
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A Formalization of Dedekind Domains and Class Groups of Global Fields J. Autom. Reason. (IF 1.1) Pub Date : 2022-09-08 Anne Baanen, Sander R. Dahmen, Ashvni Narayanan, Filippo A. E. Nuccio Mortarino Majno di Capriglio
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Faster Linear Unification Algorithm J. Autom. Reason. (IF 1.1) Pub Date : 2022-08-12 Dennis de Champeaux
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From Specification to Testing: Semantics Engineering for Lua 5.2 J. Autom. Reason. (IF 1.1) Pub Date : 2022-08-11 Mallku Soldevila, Beta Ziliani, Bruno Silvestre
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A Formalization of SQL with Nulls J. Autom. Reason. (IF 1.1) Pub Date : 2022-07-27 Wilmer Ricciotti, James Cheney
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Tuple Interpretations for Termination of Term Rewriting J. Autom. Reason. (IF 1.1) Pub Date : 2022-07-25 Akihisa Yamada
Interpretation methods constitute a foundation of the termination analysis of term rewriting. From time to time, remarkable instances of interpretation methods appeared, such as polynomial interpretations, matrix interpretations, arctic interpretations, and their variants. In this paper, we introduce a general framework, the tuple interpretation method, that subsumes these variants as well as many
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Fast Left Kan Extensions Using the Chase J. Autom. Reason. (IF 1.1) Pub Date : 2022-07-06 Joshua Meyers, David I. Spivak, Ryan Wisnesky
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A Comprehensive Framework for Saturation Theorem Proving J. Autom. Reason. (IF 1.1) Pub Date : 2022-06-07 Uwe Waldmann, Sophie Tourret, Simon Robillard, Jasmin Blanchette
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A Formalization of the Smith Normal Form in Higher-Order Logic J. Autom. Reason. (IF 1.1) Pub Date : 2022-05-26 Jose Divasón, René Thiemann
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Set of Support, Demodulation, Paramodulation: A Historical Perspective J. Autom. Reason. (IF 1.1) Pub Date : 2022-05-24 Maria Paola Bonacina
This article is a tribute to the scientific legacy of automated reasoning pioneer and JAR founder Lawrence T. (Larry) Wos. Larry’s main technical contributions were the set-of-support strategy for resolution theorem proving, and the demodulation and paramodulation inference rules for building equality into resolution. Starting from the original definitions of these concepts in Larry’s papers, this
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Local is Best: Efficient Reductions to Modal Logic K J. Autom. Reason. (IF 1.1) Pub Date : 2022-05-23 Fabio Papacchini, Cláudia Nalon, Ullrich Hustadt, Clare Dixon
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Theorem Proving as Constraint Solving with Coherent Logic J. Autom. Reason. (IF 1.1) Pub Date : 2022-05-20 Predrag Janičić, Julien Narboux
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Combination of Uniform Interpolants via Beth Definability J. Autom. Reason. (IF 1.1) Pub Date : 2022-05-12 Diego Calvanese, Silvio Ghilardi, Alessandro Gianola, Marco Montali, Andrey Rivkin
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Deciding the Word Problem for Ground and Strongly Shallow Identities w.r.t. Extensional Symbols J. Autom. Reason. (IF 1.1) Pub Date : 2022-05-07 Franz Baader, Deepak Kapur
The word problem for a finite set of ground identities is known to be decidable in polynomial time using congruence closure, and this is also the case if some of the function symbols are assumed to be commutative or defined by certain shallow identities, called strongly shallow. We show that decidability in P is preserved if we add the assumption that certain function symbols f are extensional in the