Related papers: SAT Solving for Variants of First-Order Subsumptio…
Subsumption resolution is an expensive but highly effective simplifying inference for first-order saturation theorem provers. We present a new SAT-based reasoning technique for subsumption resolution, without requiring radical changes to…
Commonly used proof strategies by automated reasoners organise proof search either by ordering-based saturation or by reducing goals to subgoals. In this paper, we combine these two approaches and advocate a SAT-based method with symmetry…
Fundamentally, every static program analyser searches for a proof through a combination of heuristics providing candidate solutions and a candidate validation technique. Essentially, the heuristic reduces a second-order problem to a…
Complex logical reasoning tasks require a long sequence of reasoning, which a large language model (LLM) with chain-of-thought prompting still falls short. To alleviate this issue, neurosymbolic approaches incorporate a symbolic solver.…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
Over the last few decades, many distinct lines of research aimed at automating mathematics have been developed, including computer algebra systems (CASs) for mathematical modelling, automated theorem provers for first-order logic, SAT/SMT…
Motivated by applications of first-order theorem proving to software analysis, we introduce a new inference rule, called subsumption demodulation, to improve support for reasoning with conditional equalities in superposition-based theorem…
This work extends the existing MACE-style finite model finding approach to multi-sorted first order logic. This existing approach iteratively assumes increasing domain sizes and encodes the related ground problem as a SAT problem. When…
CNF-based SAT and MaxSAT solvers are central to logic synthesis and verification systems. The increasing popularity of these constraint problems in electronic design automation encourages studies on different SAT problems and their…
Satisfiability-based automated reasoning is an approach that is being successfully used in software engineering to validate complex software, including for safety-critical systems. Such reasoning underlies many validation activities, from…
This paper introduces a propositional encoding for lexicographic path orders in connection with dependency pairs. This facilitates the application of SAT solvers for termination analysis of term rewrite systems based on the dependency pair…
Verifying software correctness has always been an important and complicated task. Recently, formal proofs of critical properties of algorithms and even implementations are becoming practical. Currently, the most powerful automated proof…
State-of-the-art algorithms for industrial instances of MaxSAT problem rely on iterative calls to a SAT solver. Preprocessing is crucial for the acceleration of SAT solving, and the key preprocessing techniques rely on the application of…
Sorting networks are oblivious sorting algorithms with many practical applications and rich theoretical properties. Propositional encodings of sorting networks are a key tool for proving concrete bounds on the minimum number of comparators…
On the one hand, Constraint Satisfaction Problems allow one to declaratively model problems. On the other hand, propositional satisfiability problem (SAT) solvers can handle huge SAT instances. We thus present a technique to declaratively…
Over the last two decades, propositional satisfiability (SAT) has become one of the most successful and widely applied techniques for the solution of NP-complete problems. The aim of this paper is to investigate theoretically how Sat can be…
SAT provers are powerful tools for solving real-sized logic problems, but using them requires solid programming knowledge and may be seen w.r.t.\ logic like assembly language w.r.t.\ programming. Something like a high level language was…
Logic-based abduction finds important applications in artificial intelligence and related areas. One application example is in finding explanations for observed phenomena. Propositional abduction is a restriction of abduction to the…
Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…
Semi-algebraic proof systems such as sum-of-squares (SoS) have attracted a lot of attention recently due to their relation to approximation algorithms: constant degree semi-algebraic proofs lead to conjecturally optimal polynomial-time…