Related papers: Closing a Gap in the Complexity of Refinement Moda…
We introduce the completeness problem for Modal Logic and examine its complexity. For a definition of completeness for formulas, given a formula of a modal logic, the completeness problem asks whether the formula is complete for that logic.…
Modal logics are widely used in computer science. The complexity of modal satisfiability problems has been investigated since the 1970s, usually proving results on a case-by-case basis. We prove a very general classification for a wide…
Motivated by description logics, we investigate what happens to the complexity of modal satisfiability problems if we only allow formulas built from literals, $\wedge$, $\Diamond$, and $\Box$. Previously, the only known result was that the…
Iterative abstraction refinement techniques are one of the most prominent paradigms for the analysis and verification of systems with large or infinite state spaces. This paper investigates the changes of truth values of system properties…
Graded modal logic is the formal language obtained from ordinary (propositional) modal logic by endowing its modal operators with cardinality constraints. Under the familiar possible-worlds semantics, these augmented modal operators receive…
Temporal Equilibrium Logic (TEL) is a promising framework that extends the knowledge representation and reasoning capabilities of Answer Set Programming with temporal operators in the style of LTL. To our knowledge it is the first…
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…
Standpoint linear temporal logic SLTL is a recent formalism able to model possibly conflicting commitments made by distinct agents, taking into account aspects of temporal reasoning. In this paper, we analyse the computational properties of…
We study the computational complexity of model checking and satisfiability problems of polyadic modal logics extended with permutations and Boolean operators on accessibility relations. First, we show that the combined complexity of the…
Large language models (LLMs) show strong performance across natural language processing (NLP), mathematical reasoning, and programming, and recent large reasoning models (LRMs) further emphasize explicit reasoning. Yet their computational…
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…
Autoformalization, which translates natural language mathematics into machine-verifiable formal statements, is critical for using formal mathematical reasoning to solve math problems stated in natural language. While Large Language Models…
Metric Interval Temporal Logic (MITL) is a well studied real-time, temporal logic that has decidable satisfiability and model checking problems. The decision procedures for MITL rely on the automata theoretic approach, where logic formulas…
For lack of general algorithmic methods that apply to wide classes of logics, establishing a complexity bound for a given modal logic is often a laborious task. The present work is a step towards a general theory of the complexity of modal…
Reasoning has emerged as the next major frontier for language models (LMs), with rapid advances from both academic and industrial labs. However, this progress often outpaces methodological rigor, with many evaluations relying on…
Linear and semidefinite programming (LP, SDP), regularisation through basis pursuit (BP) and Lasso have seen great success in mathematics, statistics, data science, computer-assisted proofs and learning. The success of LP is traditionally…
It is known that many modal and superintuitionistic logics are PSPACE-hard in languages with a small number of variables; however, questions about the complexity of similar fragments of many logics obtained by adding various axioms to…
We present a PSPACE algorithm that decides satisfiability of the graded modal logic Gr(K_R)---a natural extension of propositional modal logic K_R by counting expressions---which plays an important role in the area of knowledge…
Let L be some extension of classical propositional logic. The non-iterated probabilistic logic over L, is the logic PL that is defined by adding non-nested probabilistic operators in the language of L. For example in PL we can express a…
Linear programming (LP) relaxations are widely employed in exact solution methods for multilinear programs (MLP). One example is the family of Recursive McCormick Linearization (RML) strategies, where bilinear products are substituted for…