Related papers: Satisfiability.jl: Satisfiability Modulo Theories …
Natural language understanding requires interleaving textual and logical reasoning, yet large language models often fail to perform such reasoning reliably. Existing neurosymbolic systems combine LLMs with solvers but remain limited to…
Machine learning is a thriving part of computer science. There are many efficient approaches to machine learning that do not provide strong theoretical guarantees, and a beautiful general learning theory. Unfortunately, machine learning…
Answer set programming (ASP) is a paradigm for declarative problem solving where problems are first formalized as rule sets, i.e., answer-set programs, in a uniform way and then solved by computing answer sets for programs. The…
In this paper, we study the problem of formal verification for Answer Set Programming (ASP), namely, obtaining a formal proof showing that the answer sets of a given (non-ground) logic program P correctly correspond to the solutions to the…
The combination of uninterpreted function symbols and universal quantification occurs in many applications of automated reasoning, for example, due to their ability to reason about arrays. Yet the satisfiability of such formulas is, in…
Virtually all verification techniques using formal methods rely on the availability of a formal specification, which describes the design requirements precisely. However, formulating specifications remains a manual task that is notoriously…
Many SMT solvers implement efficient SAT-based procedures for solving fixed-size bit-vector formulas. These approaches, however, cannot be used directly to reason about bit-vectors of symbolic bit-width. To address this shortcoming, we…
Efforts to apply transformer-based language models (TLMs) to the problem of reasoning in natural language have enjoyed ever-increasing success in recent years. The most fundamental task in this area to which nearly all others can be reduced…
We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality…
This paper accompanies a new dataset of non-linear real arithmetic problems for the SMT-LIB benchmark collection. The problems come from an automated proof procedure of Gerhold--Kauers, which is well suited for solution by SMT. The problems…
Metric Temporal Logic (MTL) is a prominent specification formalism for real-time systems. In this paper, we show that the satisfiability problem for MTL over finite timed words is decidable, with non-primitive recursive complexity. We also…
Satisfiability Modulo Linear Integer Arithmetic, SMT(LIA) for short, is pivotal across various critical domains. Previous research has primarily focused on SMT solving techniques. However, in practical applications such as software and…
In this paper, we address the problem of the (reactive) realizability of specifications of theories richer than Booleans, including arithmetic theories. Our approach transforms theory specifications into purely Boolean specifications by (1)…
We give an overview of recent techniques for implementing syntax-guided synthesis (SyGuS) algorithms in the core of Satisfiability Modulo Theories (SMT) solvers. We define several classes of synthesis conjectures and corresponding…
We consider here Linear Temporal Logic (LTL) formulas interpreted over \emph{finite} traces. We denote this logic by LTLf. The existing approach for LTLf satisfiability checking is based on a reduction to standard LTL satisfiability…
We present MsATL: the first tool for deciding the satisfiability of Alternating-time Temporal Logic (ATL) with imperfect information. MsATL combines SAT Modulo Monotonic Theories solvers with existing ATL model checkers: MCMAS and STV. The…
The paper focuses on the automatic generating of the witnesses for the word equation satisfiability problem by means of specializing an interpreter which tests whether a composition of variable substitutions of a given word equation system…
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 present the logic iJT4, which is an explicit version of intuitionistic S4 and establish soundness and completeness with respect to modular models.
Financial regulations are increasingly complex, hindering automated compliance-especially the maintenance of logical consistency with minimal human oversight. We introduce a Neuro-Symbolic Compliance Framework that integrates Large Language…