Related papers: A general proof system for logics of imperfect inf…
Given the intractably large size of the space of proofs, any model that is capable of general deductive reasoning must generalize to proofs of greater complexity. Recent studies have shown that large language models (LLMs) possess some…
Justification theory is a unifying framework for semantics of non-monotonic logics. It is built on the notion of a justification, which intuitively is a graph that explains the truth value of certain facts in a structure. Knowledge…
Computability logic is a formal theory of computability. The earlier article "Introduction to cirquent calculus and abstract resource semantics" by Japaridze proved soundness and completeness for the basic fragment CL5 of computability…
Program verification is to develop the program's proof system, and to prove the proof system soundness with respect to a trusted operational semantics of the program. However, many practical program verifiers are not based on operational…
The work reported here introduces Defeasible Logic Programming (DeLP), a formalism that combines results of Logic Programming and Defeasible Argumentation. DeLP provides the possibility of representing information in the form of weak rules…
Inferring from inconsistency and making decisions are two problems which have always been treated separately by researchers in Artificial Intelligence. Consequently, different models have been proposed for each category. Different…
We describe a representation and a set of inference methods that combine logic programming techniques with probabilistic network representations for uncertainty (influence diagrams). The techniques emphasize the dynamic construction and…
The paper presents a method for obtaining problems whose conclusions contain disjunctive propositions. These problems constitute a version of inverse problems with a given logical structure. The logical models in the groups of problems…
In this paper we investigate the complexity-theoretical aspects of cyclic and non-wellfounded proofs in the context of parsimonious logic, a variant of linear logic where the exponential modality ! is interpreted as a constructor for…
In our previous series of studies to investigate the role of evidential reasoning in the RUBRIC system for full-text document retrieval (Tong et al., 1985; Tong and Shapiro, 1985; Tong and Appelbaum, 1987), we identified the important role…
This paper analyzes the correctness of the subsumption algorithm used in CLASSIC, a description logic-based knowledge representation system that is being used in practical applications. In order to deal efficiently with individuals in…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
In everyday life it happens that a person has to reason about what other people think and how they behave, in order to achieve his goals. In other words, an individual may be required to adapt his behaviour by reasoning about the others'…
This paper explores proof-theoretic aspects of hybrid type-logical grammars , a logic combining Lambek grammars with lambda grammars. We prove some basic properties of the calculus, such as normalisation and the subformula property and also…
In this paper we present a formalization of Intuitionistic Propositional Logic in the Lean proof assistant. Our approach focuses on verifying two completeness proofs for the studied logical system, as well as exploring the relation between…
A significant amount of information in today's world is stored in structured and semi-structured knowledge bases. Efficient and simple methods to query them are essential and must not be restricted to only those who have expertise in formal…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
The paper proposes an analysis on some existent ontologies, in order to point out ways to resolve semantic heterogeneity in information systems. Authors are highlighting the tasks in a Knowledge Acquisiton System and identifying aspects…
We describe a variant of resolution rule of proof and show that it is complete for stable semantics of logic programs. We show applications of this result.
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…