A sequent calculus for reasoning in four-valued Description Logics

1997 ◽  
pp. 343-357 ◽  
Author(s):  
Umberto Straccia
Keyword(s):  
Sequent Calculus ◽  
Description Logics

scholarly journals Sequent calculus as a compiler intermediate language

2016 ◽  
Vol 51 (9) ◽  
pp. 74-88 ◽  
Author(s):  
Paul Downen ◽  
Luke Maurer ◽  
Zena M. Ariola ◽  
Simon Peyton Jones
Keyword(s):  
Sequent Calculus ◽  
Intermediate Language

scholarly journals On the relation between keys and link keys for data interlinking

Semantic Web ◽  
2020 ◽  
pp. 1-21
Author(s):  
Manuel Atencia ◽  
Jérôme David ◽  
Jérôme Euzenat
Keyword(s):  
Description Logics ◽  
The Other ◽  
Formal Framework ◽  
Precise Relationship

Both keys and their generalisation, link keys, may be used to perform data interlinking, i.e. finding identical resources in different RDF datasets. However, the precise relationship between keys and link keys has not been fully determined yet. A common formal framework encompassing both keys and link keys is necessary to ensure the correctness of data interlinking tools based on them, and to determine their scope and possible overlapping. In this paper, we provide a semantics for keys and link keys within description logics. We determine under which conditions they are legitimate to generate links. We provide conditions under which link keys are logically equivalent to keys. In particular, we show that data interlinking with keys and ontology alignments can be reduced to data interlinking with link keys, but not the other way around.

scholarly journals Deduction in Non-Fregean Propositional Logic SCI

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 115 ◽  
Author(s):  
Joanna Golińska-Pilarek ◽  
Magdalena Welle
Keyword(s):  
Propositional Logic ◽  
Sequent Calculus ◽  
Classical Propositional Logic ◽  
Tableau System ◽  
Soundness And Completeness

We study deduction systems for the weakest, extensional and two-valued non-Fregean propositional logic SCI . The language of SCI is obtained by expanding the language of classical propositional logic with a new binary connective ≡ that expresses the identity of two statements; that is, it connects two statements and forms a new one, which is true whenever the semantic correlates of the arguments are the same. On the formal side, SCI is an extension of classical propositional logic with axioms characterizing the identity connective, postulating that identity must be an equivalence and obey an extensionality principle. First, we present and discuss two types of systems for SCI known from the literature, namely sequent calculus and a dual tableau-like system. Then, we present a new dual tableau system for SCI and prove its soundness and completeness. Finally, we discuss and compare the systems presented in the paper.

A Set-theoretic Approach to Reasoning Services for the Description Logic 𝒟 ℒ D 4,×

2020 ◽  
Vol 176 (3-4) ◽  
pp. 349-384
Author(s):  
Domenico Cantone ◽  
Marianna Nicolosi-Asmundo ◽  
Daniele Francesco Santamaria
Keyword(s):  
Description Logic ◽  
Description Logics ◽  
Theoretic Approach ◽  
The Novel ◽  
Data Types ◽  
Left Hand ◽  
Rule Languages ◽  
Tableau System ◽  
High Scalability ◽  
Better Than

In this paper we consider the most common TBox and ABox reasoning services for the description logic 𝒟ℒ〈4LQSR,x〉(D) ( 𝒟 ℒ D 4,× , for short) and prove their decidability via a reduction to the satisfiability problem for the set-theoretic fragment 4LQSR. 𝒟 ℒ D 4,× is a very expressive description logic. It combines the high scalability and efficiency of rule languages such as the SemanticWeb Rule Language (SWRL) with the expressivity of description logics. In fact, among other features, it supports Boolean operations on concepts and roles, role constructs such as the product of concepts and role chains on the left-hand side of inclusion axioms, role properties such as transitivity, symmetry, reflexivity, and irreflexivity, and data types. We further provide a KE-tableau-based procedure that allows one to reason on the main TBox and ABox reasoning tasks for the description logic 𝒟 ℒ D 4,× . Our algorithm is based on a variant of the KE-tableau system for sets of universally quantified clauses, where the KE-elimination rule is generalized in such a way as to incorporate the γ-rule. The novel system, called KEγ-tableau, turns out to be an improvement of the system introduced in [1] and of standard first-order KE-tableaux [2]. Suitable benchmark test sets executed on C++ implementations of the three mentioned systems show that in several cases the performances of the KEγ-tableau-based reasoner are up to about 400% better than the ones of the other two systems.

scholarly journals On Polymorphic Sessions and Functions

2021 ◽  
Vol 43 (2) ◽  
pp. 1-55
Author(s):  
Bernardo Toninho ◽  
Nobuko Yoshida
Keyword(s):  
Natural Deduction ◽  
Sequent Calculus ◽  
Linear Logic ◽  
Linear Formulation ◽  
Session Types ◽  
Logical Foundation ◽  
Π Calculus ◽  
Soundness And Completeness ◽  
System F ◽  
Algebraic Representations

This work exploits the logical foundation of session types to determine what kind of type discipline for the Λ-calculus can exactly capture, and is captured by, Λ-calculus behaviours. Leveraging the proof theoretic content of the soundness and completeness of sequent calculus and natural deduction presentations of linear logic, we develop the first mutually inverse and fully abstract processes-as-functions and functions-as-processes encodings between a polymorphic session π-calculus and a linear formulation of System F. We are then able to derive results of the session calculus from the theory of the Λ-calculus: (1) we obtain a characterisation of inductive and coinductive session types via their algebraic representations in System F; and (2) we extend our results to account for value and process passing, entailing strong normalisation.

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