Related papers: Twist your logic with TouIST
We present here a new explicit reasoning framework for linear temporal logic (LTL), which is built on top of propositional satisfiability (SAT) solving. As a proof-of-concept of this framework, we describe a new LTL satisfiability tool,…
Integrating logical reasoning within deep learning architectures has been a major goal of modern AI systems. In this paper, we propose a new direction toward this goal by introducing a differentiable (smoothed) maximum satisfiability…
Satisfiability modulo theory (SMT) consists in testing the satisfiability of first-order formulas over linear integer or real arithmetic, or other theories. In this survey, we explain the combination of propositional satisfiability and…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
Automatically generating high-quality step-by-step solutions to math word problems has many applications in education. Recently, combining large language models (LLMs) with external tools to perform complex reasoning and calculation has…
Reconfiguration aims at recovering a system from a fault by automatically adapting the system configuration, such that the system goal can be reached again. Classical approaches typically use a set of pre-defined faults for which…
In recent years, portfolio approaches to solving SAT problems and CSPs have become increasingly common. There are also a number of different encodings for representing CSPs as SAT instances. In this paper, we leverage advances in both SAT…
Propositional satisfiability (SAT) solvers, which typically operate using conjunctive normal form (CNF), have been successfully applied in many domains. However, in some application areas such as circuit verification, bounded model…
A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…
The paper focuses on the automatic generating of the witnesses for the word equation satisfiability problem by means of specializing an interpreter which tests whether a composition of variable substitutions of a given word equation system…
Proof assistants play a dual role as programming languages and logical systems. As programming languages, proof assistants offer standard modularity mechanisms such as first-class functions, type polymorphism and modules. As logical…
Test-time scaling (TTS) has emerged as a new frontier for scaling the performance of Large Language Models. In test-time scaling, by using more computational resources during inference, LLMs can improve their reasoning process and task…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
Legal syllogism is a form of deductive reasoning commonly used by legal professionals to analyze cases. In this paper, we propose legal syllogism prompting (LoT), a simple prompting method to teach large language models (LLMs) for legal…
Large language models (LLMs) often struggle with complex logical reasoning due to logical inconsistencies and the inherent difficulty of such reasoning. We use Lean, a theorem proving framework, to address these challenges. By formalizing…
Satisfiability modulo theories (SMT) solvers have throughout the years been able to cope with increasingly expressive formulas, from ground logics to full first-order logic modulo theories. Nevertheless, higher-order logic within SMT is…
#SMT, or model counting for logical theories, is a well-known hard problem that generalizes such tasks as counting the number of satisfying assignments to a Boolean formula and computing the volume of a polytope. In the realm of…
Weighted Max-SAT is the optimization version of SAT and many important problems can be naturally encoded as such. Solving weighted Max-SAT is an important problem from both a theoretical and a practical point of view. In recent years, there…
We present here a SAT-based framework for LTLf (Linear Temporal Logic on Finite Traces) satisfiability checking. We use propositional SAT-solving techniques to construct a transition system for the input LTLf formula; satisfiability…
Logic-based abduction finds important applications in artificial intelligence and related areas. One application example is in finding explanations for observed phenomena. Propositional abduction is a restriction of abduction to the…