Related papers: MALL proof equivalence is Logspace-complete, via b…
Large language models (LLMs) demonstrate considerable potential in various natural language tasks but face significant challenges in mathematical reasoning, particularly in executing precise, multi-step logic. However, current evaluation…
The equivalence test is a main part in any classification problem. It helps to prove bounds for the main parameters of the considered combinatorial structures and to study their properties. In this paper, we present algorithms for…
Formal theories of arithmetic have traditionally been based on either classical or intuitionistic logic, leading to the development of Peano and Heyting arithmetic, respectively. We propose to use $\mu$MALL as a formal theory of arithmetic…
Large Language Models (LLMs) achieve strong performance on logical reasoning benchmarks, yet their reliability remains uncertain. Existing evaluations rely on static benchmarks, which fail to assess robustness under logically equivalent…
Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classical linear propositional logic caught by proof nets. This…
We present an extension to the quantifier-free theory of integer arrays which allows us to express counting. The properties expressible in Array Folds Logic (AFL) include statements such as "the first array cell contains the array length,"…
Similarity learning is a general problem to elicit useful representations by predicting the relationship between a pair of patterns. This problem is related to various important preprocessing tasks such as metric learning, kernel learning,…
Boolean matching is an important problem in logic synthesis and verification. Despite being well-studied for conventional Boolean circuits, its treatment for reversible logic circuits remains largely, if not completely, missing. This work…
The constraint satisfaction problem (CSP) and its quantified extensions, whether without (QCSP) or with disjunction (QCSP_or), correspond naturally to the model checking problem for three increasingly stronger fragments of positive…
Program verification is to develop the program's proof system, and to prove the proof system soundness with respect to a trusted operational semantics of the program. However, many practical program verifiers are not based on operational…
In this paper, we develop a quantified propositional proof systems that corresponds to logarithmic-space reasoning. We begin by defining a class SigmaCNF(2) of quantified formulas that can be evaluated in log space. Then our new proof…
We study the logic FO(~), the extension of first-order logic with team semantics by unrestricted Boolean negation. It was recently shown axiomatizable, but otherwise has not yet received much attention in questions of computational…
Probabilistic systems are an important theme in AI domain. As the specification language, the logic PCTL is now the default logic for reasoning about probabilistic properties. In this paper, we present a natural and succinct probabilistic…
Polynomial multiplication is known to have quasi-linear complexity in both the dense and the sparse cases. Yet no truly linear algorithm has been given in any case for the problem, and it is not clear whether it is even possible. This…
The topological interpretation of modal logics provides descriptive languages and proof systems for reasoning about points of topological spaces. Recent work has been devoted to model checking of spatial logics on discrete spatial…
The proof identity problem asks: When are two proofs the same? The question naturally occurs when one reflects on mathematical practice. The problem understandably can be seen as a challenge for mathematical logic, and indeed various…
This paper studies Linear Temporal Logic over Finite Traces (LTLf) where proposition letters are replaced with first-order formulas interpreted over arbitrary theories, in the spirit of Satisfiability Modulo Theories. The resulting logic,…
It has been shown in the late 1960s that each formula of first-order logic without constants and function symbols obeys a zero-one law: As the number of elements of finite models increases, every formula holds either in almost all or in…
Equilibrium logic is an approach to nonmonotonic reasoning that extends the stable-model and answer-set semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations…
We study complexity of the model-checking problems for LTL with registers (also known as freeze LTL) and for first-order logic with data equality tests over one-counter automata. We consider several classes of one-counter automata (mainly…