Related papers: SAT Solving for Variants of First-Order Subsumptio…
We present two different methods for estimating the cost of solving SAT problems. The methods focus on the online behaviour of the backtracking solver, as well as the structure of the problem. Modern SAT solvers present several challenges…
To support reasoning about properties of programs operating with boolean values one needs theorem provers to be able to natively deal with the boolean sort. This way, program properties can be translated to first-order logic and theorem…
This paper presents a novel SAT-based approach for the computation of extensions in abstract argumentation, with focus on preferred semantics, and an empirical evaluation of its performances. The approach is based on the idea of reducing…
Exploitation of symmetries is an indispensable approach to solve certain classes of difficult SAT instances. Numerous techniques for the use of symmetry in SAT have evolved over the past few decades. But no matter how symmetries are used…
Large Reasoning Models (LRMs) have revolutionized complex problem-solving, yet they exhibit a pervasive "overthinking", generating unnecessarily long reasoning chains. While current solutions improve token efficiency, they often sacrifice…
Several paradigms for declarative problem solving start from a specification in a high-level language, which is then transformed to a low-level language, such as SAT or SMT. Often, this transformation includes a "grounding" step to remove…
The past three decades have witnessed notable success in designing efficient SAT solvers, with modern solvers capable of solving industrial benchmarks containing millions of variables in just a few seconds. The success of modern SAT solvers…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…
Deep learning techniques lie at the heart of several significant AI advances in recent years including object recognition and detection, image captioning, machine translation, speech recognition and synthesis, and playing the game of Go.…
Modern software for propositional satisfiability problems gives a powerful automated reasoning toolkit, capable of outputting not only a satisfiable/unsatisfiable signal but also a justification of unsatisfiability in the form of resolution…
The theory of finite term algebras provides a natural framework to describe the semantics of functional languages. The ability to efficiently reason about term algebras is essential to automate program analysis and verification for…
Answer Set Programming (ASP) is an important logic programming paradigm within the field of Knowledge Representation and Reasoning. As a concise, human-readable, declarative language, ASP is an excellent tool for developing trustworthy…
In the last two decades, modal and description logics have been applied to numerous areas of computer science, including knowledge representation, formal verification, database theory, distributed computing and, more recently, semantic web…
Abstract solvers are a method to formally analyze algorithms that have been profitably used for describing, comparing and composing solving techniques in various fields such as Propositional Satisfiability (SAT), Quantified SAT,…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
We present an automated reasoning framework for synthesizing recursion-free programs using saturation-based theorem proving. Given a functional specification encoded as a first-order logical formula, we use a first-order theorem prover to…
Satisfiability Modulo Theories (SMT) and SAT solvers are critical components in many formal software tools, primarily due to the fact that they are able to easily solve logical problem instances with millions of variables and clauses. This…
Assumption-based argumentation (ABA) is a central structured argumentation formalism. As shown recently, answer set programming (ASP) enables efficiently solving NP-hard reasoning tasks of ABA in practice, in particular in the commonly…
Verification methods based on SAT, SMT, and Theorem Proving often rely on proofs of unsatisfiability as a powerful tool to extract information in order to reduce the overall effort. For example a proof may be traversed to identify a minimal…
Large Language Models (LLMs) still struggle with complex logical reasoning. While previous works achieve remarkable improvements, their performance is highly dependent on the correctness of translating natural language (NL) problems into a…