相关论文: Complexity of Reasoning with Cardinality Minimalit…

In this short paper we present a survey of some results concerning the random SAT problems. To elaborate, the Boolean Satisfiability (SAT) Problem refers to the problem of determining whether a given set of $m$ Boolean constraints over $n$…

Answer-set programming (ASP) paradigm is a way of using logic to solve search problems. Given a search problem, to solve it one designs a theory in the logic so that models of this theory represent problem solutions. To compute a solution…

This paper explores the relationship of artificial intelligence to the task of resolving open questions in mathematics. We first present an updated version of a traditional argument that limitative results from computability and complexity…

Logic provides a controlled testbed for evaluating LLM-based reasoners, yet standard SAT-style benchmarks often conflate surface difficulty (length, wording, clause order) with the structural phenomena that actually determine…

Computational complexity has often been ignored in philosophy of mind, in philosophical artificial intelligence studies. The purpose of this paper is threefold. First and foremost, to show the importance of complexity rather than…

We investigate the computational complexity of the satisfiability problem of modal inclusion logic. We distinguish two variants of the problem: one for the strict and another one for the lax semantics. Both problems turn out to be…

Chain-of-Thought (CoT) prompting plays an indispensable role in endowing large language models (LLMs) with complex reasoning capabilities. However, CoT currently faces two fundamental challenges: (1) Sufficiency, which ensures that the…

Different types of reasoning impose different structural demands on representational systems, yet no systematic account of these demands exists across psychology, AI, and philosophy of mind. I propose a framework identifying four structural…

We introduce SATBench, a benchmark for evaluating the logical reasoning capabilities of large language models (LLMs) through logical puzzles derived from Boolean satisfiability (SAT) problems. Unlike prior work that focuses on inference…

Logic Artificial Intelligence (AI) is a subfield of AI where variables can take two defined arguments, True or False, and are arranged in clauses that follow the rules of formal logic. Several problems that span from physical systems to…

This paper establishes a theoretical foundation for understanding the fundamental limits of AI explainability through algorithmic information theory. We formalize explainability as the approximation of complex models by simpler ones,…

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…

This note considers checking satisfiability of sets of propositional clauses (SAT instances). It shows that "unipolar sets" of clauses (containing no positive or no negative clauses) provide an "early sign" of satisfiability of SAT…

Mathematical understanding and reasoning are crucial tasks for assessing the capabilities of artificial intelligence (AI). However, existing benchmarks either require just a few steps of reasoning, or only contain a small amount of data in…

Autoepistemic logic extends propositional logic by the modal operator L. A formula that is preceded by an L is said to be "believed". The logic was introduced by Moore 1985 for modeling an ideally rational agent's behavior and reasoning…

The amount of information in satisfiability problem (SAT) is considered. SAT can be polynomial-time solvable when the solving algorithm holds an exponential amount of information. It is also established that SAT Kolmogorov complexity is…

Decision-making systems based on AI and machine learning have been used throughout a wide range of real-world scenarios, including healthcare, law enforcement, education, and finance. It is no longer far-fetched to envision a future where…

Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…

We abstractly formulate an analytic problem that arises naturally in the study of coordination in multi-agent systems. Let I be a set of arbitrary cardinality (the set of actions) and assume that for each pair of distinct actions (i,j), we…

Applying deep learning to solve real-life instances of hard combinatorial problems has tremendous potential. Research in this direction has focused on the Boolean satisfiability (SAT) problem, both because of its theoretical centrality and…