Related papers: Twist your logic with TouIST
The complexity class $NP$ can be logically characterized both through existential second order logic $SO\exists$, as proven by Fagin, and through simulating a Turing machine via the satisfiability problem of propositional logic SAT, as…
The most common ways to explore latent document dimensions are topic models and clustering methods. However, topic models have several drawbacks: e.g., they require us to choose the number of latent dimensions a priori, and the results are…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
Existing math datasets evaluate the reasoning abilities of large language models (LLMs) by either using the final answer or the intermediate reasoning steps derived from static examples. However, the former approach fails to surface model's…
Satisfiability Modulo Counting (SMC) is a recently proposed general language to reason about problems integrating statistical and symbolic Artificial Intelligence. An SMC problem is an extended SAT problem in which the truth values of a few…
Fact verification on tabular evidence incentivises the use of symbolic reasoning models where a logical form is constructed (e.g. a LISP-style program), providing greater verifiability than fully neural approaches. However, these systems…
Boolean satisfiability (SAT) is a fundamental NP-complete problem with many applications, including automated planning and scheduling. To solve large instances, SAT solvers have to rely on heuristics, e.g., choosing a branching variable in…
In this paper, by constructing extremely hard examples of CSP (with large domains) and SAT (with long clauses), we prove that such examples cannot be solved without exhaustive search, which is stronger than P $\neq$ NP. This constructive…
This paper introduces the 2019 version of \us{}, a novel Constraint Programming framework for floating point verification problems expressed with the SMT language of SMTLIB. SMT solvers decompose their task by delegating to specific…
Large Language Models (LLMs) still struggle with complex logical reasoning. While previous works achieve remarkable improvements, their performance is highly dependent on the correctness of translating natural language (NL) problems into a…
Boolean Satisfiability (SAT) solvers are now routinely used in the verification of large industrial problems. However, their application in safety-critical domains such as the railways, avionics, and automotive industries requires some form…
Training models through self-play alone (without any human data) has been a longstanding goal in AI, but its effectiveness for training large language models remains unclear, particularly in code generation where rewards based on unit tests…
Formal reasoning about finite sets and cardinality is an important tool for many applications, including software verification, where very often one needs to reason about the size of a given data structure and not only about what its…
Automated verification tools based on SMT solvers have made significant progress in verifying complex software systems. However, these tools face a fundamental tension between automation and performance when dealing with quantifier…
This study presents a novel learning approach designed to enhance both mathematical reasoning and problem-solving abilities of Large Language Models (LLMs). We focus on integrating the Chain-of-Thought (CoT) and the Program-of-Thought (PoT)…
Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to…
We propose prioritized unit propagation with periodic resetting, which is a simple but surprisingly effective algorithm for solving random SAT instances that are meant to be hard. In particular, an evaluation on the Random Track of the 2017…
Multimodal Large Language Models (MLLMs) have demonstrated remarkable reasoning capabilities across modalities such as images and text. However, tabular data, despite being a critical real-world modality, remains relatively underexplored in…
Interference is a phenomenon on proof systems for SAT solving that is both counter-intuitive and bothersome when developing proof-logging techniques. However, all existing proof systems that can produce short proofs for all inprocessing…