Related papers: Twist your logic with TouIST
Complex reasoning aims to draw a correct inference based on complex rules. As a hallmark of human intelligence, it involves a degree of explicit reading comprehension, interpretation of logical knowledge and complex rule application. In…
Large Reasoning Models (LRMs) have revolutionized complex problem-solving, yet they exhibit a pervasive "overthinking", generating unnecessarily long reasoning chains. While current solutions improve token efficiency, they often sacrifice…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there is constraint logic programming which computes a solution as an answer substitution to a query containing the…
We present a simple programming language based on G\"odel numbering and prime factorization, enhanced with explicit, scoped loops, allowing for easy program composition. Further, we will present a theorem prover that allows expressing and…
Bit-vector formulas arising from hardware verification problems often contain word-level arithmetic operations. Empirical evidence shows that state-of-the-art SMT solvers are not very efficient at reasoning about bit-vector formulas with…
Large Language Models (LLMs) for formal theorem proving have shown significant promise, yet they often lack generalizability and are fragile to even minor transformations of problem statements. To address this limitation, we introduce a…
Verification methods based on SAT, SMT, and Theorem Proving often rely on proofs of unsatisfiability as a powerful tool to extract information in order to reduce the overall effort. For example a proof may be traversed to identify a minimal…
A prototype system is described whose core functionality is, based on propositional logic, the elimination of second-order operators, such as Boolean quantifiers and operators for projection, forgetting and circumscription. This approach…
Synthesis of models and strategies is a very important problem in software engineering. The main element here is checking the satisfiability of formulae expressing the specification of a system to be implemented. This paper puts forward a…
We present Woorpje, a string solver for bounded word equations (i.e., equations where the length of each variable is upper bounded by a given integer). Our algorithm works by reformulating the satisfiability of bounded word equations as a…
In this work, we provide a systematic analysis of how large language models (LLMs) contribute to solving planning problems. In particular, we examine how LLMs perform when they are used as problem solver, solution verifier, and heuristic…
In this paper, we present a novel algorithm to solve the Boolean Satisfiability (SAT) problem, using noise-based logic (NBL). Contrary to what the name may suggest, NBL is not a random/fuzzy logic system. In fact, it is a completely…
Recently, with the chain of thought (CoT) prompting, large language models (LLMs), e.g., GPT-3, have shown strong reasoning ability in several natural language processing tasks such as arithmetic, commonsense, and logical reasoning.…
We study local-search satisfiability solvers for propositional logic extended with cardinality atoms, that is, expressions that provide explicit ways to model constraints on cardinalities of sets. Adding cardinality atoms to the language of…
Justification logics are special kinds of modal logics which provide a framework for reasoning about epistemic justifications. For this, they extend classical boolean propositional logic by a family of necessity-style modal operators "t:",…
Large language models have made significant progress in various language tasks, yet they still struggle with complex mathematics. In this paper, we propose ToRA a series of Tool-integrated Reasoning Agents designed to solve challenging…
Large Language Models (LLMs) have demonstrated strong capabilities in natural language understanding and reasoning. However, their ability to perform exact, deterministic computation remains unclear. In this work, we systematically evaluate…
The dramatic improvements in combinatorial optimization algorithms over the last decades have had a major impact in artificial intelligence, operations research, and beyond, but the output of current state-of-the-art solvers is often hard…
Teaching precise mathematical reasoning can be very hard. It is very easy for a student to make a subtle mistake in a proof which invalidates it, but it is often hard for the teacher to pinpoint and explain the problem in the (often…
When working on intelligent tutor systems designed for mathematics education and its specificities, an interesting objective is to provide relevant help to the students by anticipating their next steps. This can only be done by knowing,…