The Challenge of Unifying Semantic and Syntactic Inference Restrictions

While syntactic inference restrictions don't play an important role for SAT, they are an essential reasoning technique for more expressive logics, such as first-order logic, or fragments thereof. In particular, they can result in short proofs or model representations. On the other hand, semantically guided inference systems enjoy important properties, such as the generation of solely non-redundant clauses. I discuss to what extend the two paradigms may be unifiable

Even shorter proofs without new variables

Proof formats for SAT solvers have diversified over the last decade, enabling new features such as extended resolution-like capabilities, very general extension-free rules, inclusion of proof hints, and pseudo-boolean reasoning. Interference-based methods have been proven effective, and some theoretical work has been undertaken to better explain their limits and semantics. In this work, we combine the subsumption redundancy notion from (Buss, Thapen 2019) and the overwrite logic framework from (Rebola-Pardo, Suda 2018). Natural generalizations then become apparent, enabling even shorter proofs of the pigeonhole principle (compared to those from (Heule, Kiesl, Biere 2017)) and smaller unsatisfiable core generation.Comment: 21 page

The Challenge of Unifying Semantic and Syntactic Inference Restrictions

International audienceWhile syntactic inference restrictions don't play an important role for SAT, they are an essential reasoning technique for more expressive logics, such as first-order logic, or fragments thereof. In particular, they can result in short proofs or model representations. On the other hand, semantically guided inference systems enjoy important properties, such as the generation of solely non-redundant clauses. I discuss to what extend the two paradigms may be unifiable

A Proof-Theoretic Approach to Certifying Skolemization

International audienceWhen presented with a formula to prove, most theorem provers for classical first-order logic process that formula following several steps, one of which is commonly called skolemization. That process eliminates quantifier alternation within formulas by extending the language of the underlying logic with new Skolem functions and by instantiating certain quantifiers with terms built using Skolem functions. In this paper, we address the problem of checking (i.e., certifying) proof evidence that involves Skolem terms. Our goal is to do such certification without using the mathematical concepts of model-theoretic semantics (i.e., preservation of satisfiability) and choice principles (i.e., epsilon terms). Instead , our proof checking kernel is an implementation of Gentzen's sequent calculus, which directly supports quanti-fier alternation by using eigenvariables. We shall describe deskolemization as a mapping from client-side terms, used in proofs generated by theorem provers, into kernel-side terms, used within our proof checking kernel. This mapping which associates skolemized terms to eigenvariables relies on using outer skolemization. We also point out that the removal of Skolem terms from a proof is influenced by the polarities given to propositional connectives