相关论文: Proof-theoretic aspects of paraconsistency with st…

We consider an extension of first-order logic with a recursion operator that corresponds to allowing formulas to refer to themselves. We investigate the obtained language under two different systems of semantics, thereby obtaining two…

We investigate non-wellfounded proof systems based on parsimonious logic, a weaker variant of linear logic where the exponential modality ! is interpreted as a constructor for streams over finite data. Logical consistency is maintained at a…

In deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems---such as for instance natural deduction---are applied. Therefore, the…

First-order logic is the basis for many knowledge representation formalisms and methods. Providing technological support for learning to write first-order formulas for natural language specifications requires methods to test formulas for…

A cyclic proof system is a proof system whose proof figure is a tree with cycles. The cut-elimination in a proof system is fundamental. It is conjectured that the cut-elimination in the cyclic proof system for first-order logic with…

In this paper we present the first-order logic QLETF+, a quantified version of the logic LETF+, introduced in Coniglio and Rodrigues (Studia Logica 112:561-606, 2024). QLETF+ exhibits several properties that are not always enjoyed by logics…

We study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant. Specifically, we examine the completeness of variants of classical and intuitionistic…

First-order optimization methods have attracted a lot of attention due to their practical success in many applications, including in machine learning. Obtaining convergence guarantees and worst-case performance certificates for first-order…

We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…

Paraconsistent logics constitute an important class of formalisms dealing with non-trivial reasoning from inconsistent premisses. In this paper, we introduce uniform axiomatisations for a family of nonmonotonic paraconsistent logics based…

A focused proof system provides a normal form to cut-free proofs that structures the application of invertible and non-invertible inference rules. The focused proof system of Andreoli for linear logic has been applied to both the proof…

In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The…

We present the Flow-Limited Authorization First-Order Logic (FLAFOL), a logic for reasoning about authorization decisions in the presence of information-flow policies. We formalize the FLAFOL proof system, characterize its proof-theoretic…

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…

This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…

Consistent answers to a query from a possibly inconsistent database are answers that are simultaneously retrieved from every possible repair of the database. Repairs are consistent instances that minimally differ from the original…

Given a first-order sentence, a model-checking computation tests whether the sentence holds true in a given finite structure. Data provenance extracts from this computation an abstraction of the manner in which its result depends on the…

Given two languages, a separator is a third language that contains the first one and is disjoint from the second one. We investigate the following decision problem: given two regular input languages of finite words, decide whether there…

Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…

Inspired by the efficient proof procedures discussed in {\em Computability logic} \cite{Jap03,Japic,Japfin}, we describe a heuristic proof procedure for first-order logic. This is a variant of Gentzen sequent system and has the following…