scholarly journals Proving Semantic Properties as First-Order Satisfiability (Extended Abstract)

2020 ◽  
Author(s):  
Salvador Lucas
Keyword(s):  
Logic Programming ◽  
Programming Languages ◽  
Answer Set Programming ◽  
Deductive Databases ◽  
Query Answering ◽  
Logical Theory ◽  
Data Bases ◽  
First Order ◽  
Computational Systems ◽  
Semantic Properties

The semantics of computational systems (e.g., relational and knowledge data bases, query-answering systems, programming languages, etc.) can often be expressed as (the specification of) a logical theory Th. Queries, goals, and claims about the behavior or features of the system can be expressed as formulas φ which should be checked with respect to the intended model of Th, which is often huge or even incomputable. In this paper we show how to prove such semantic properties φ of Th by just finding a model A of Th∪{φ}∪Zφ, where Zφ is an appropriate (possibly empty) theory depending on φ only. Applications to relational and deductive databases, rewriting-based systems, logic programming, and answer set programming are discussed.

Datalog Rewritability and Data Complexity of ALCHOIF with Closed Predicates

2020 ◽  
Author(s):  
Tomasz Gogacz ◽  
Sanja Lukumbuzya ◽  
Magdalena Ortiz ◽  
Mantas Šimkus
Keyword(s):  
Description Logic ◽  
Answer Set Programming ◽  
Query Answering ◽  
Stable Model ◽  
Data Complexity ◽  
First Order ◽  
Time Translation ◽  
Np Complete ◽  
Ontology Languages

We study the relative expressiveness of ontology-mediated queries (OMQs) formulated in the expressive Description Logic ALCHOIF extended with closed predicates. In particular, we present a polynomial-time translation from OMQs into Datalog with negation under the stable model semantics, the formalism that underlies Answer Set Programming. This is a novel and non-trivial result: the considered OMQs are not only non-monotonic but also feature a tricky combination of nominals, inverse roles, and role functionality. We start with atomic queries and then lift our approach to a large class of first-order queries where quantification is “guarded” by closed predicates. Our translation is based on a characterization of the query answering problem via integer programming, and a specially crafted program in Datalog with negation that finds solutions to dynamically generated systems of integer inequalities. As an important by-product of our translation, we get that the query answering problem is co-NP-complete in data complexity for the considered class of OMQs. Thus, answering these OMQs in the presence of closed predicates is not harder than answering them in the standard setting. This is not obvious as closed predicates are known to increase data complexity for some existing ontology languages.

scholarly journals Stable models for infinitary formulas with extensional atoms

2016 ◽  
Vol 16 (5-6) ◽  
pp. 771-786
Author(s):  
AMELIA HARRISON ◽  
VLADIMIR LIFSCHITZ
Keyword(s):  
Programming Languages ◽  
Answer Set Programming ◽  
Splitting Theorem ◽  
First Order ◽  
Definition Of ◽  
Stable Models ◽  
Answer Set

AbstractThe definition of stable models for propositional formulas with infinite conjunctions and disjunctions can be used to describe the semantics of answer set programming languages. In this note, we enhance that definition by introducing a distinction between intensional and extensional atoms. The symmetric splitting theorem for first-order formulas is then extended to infinitary formulas and used to reason about infinitary definitions.

scholarly journals First-order Answer Set Programming as Constructive Proof Search

2018 ◽  
Vol 18 (3-4) ◽  
pp. 673-690
Author(s):  
ALEKSY SCHUBERT ◽  
PAWEŁ URZYCZYN
Keyword(s):  
Logic Programming ◽  
Intuitionistic Logic ◽  
Proof Theory ◽  
Answer Set Programming ◽  
Theory And Practice ◽  
Close Similarity ◽  
Constructive Proof ◽  
First Order ◽  
Proof Search ◽  
Answer Set

AbstractWe propose an interpretation of the first-order answer set programming (FOASP) in terms of intuitionistic proof theory. It is obtained by two polynomial translations between FOASP and the bounded-arity fragment of the Σ1 level of the Mints hierarchy in first-order intuitionistic logic. It follows that Σ1 formulas using predicates of fixed arity (in particular unary) is of the same strength as FOASP. Our construction reveals a close similarity between constructive provability and stable entailment, or equivalently, between the construction of an answer set and an intuitionistic refutation. This paper is under consideration for publication in Theory and Practice of Logic Programming

Computing Cores for Existential Rules with the Standard Chase and ASP

2020 ◽  
Author(s):  
Markus Krötzsch
Keyword(s):  
Large Class ◽  
Data Exchange ◽  
Answer Set Programming ◽  
Query Answering ◽  
Universal Model ◽  
The Core ◽  
Universal Models ◽  
General Terms ◽  
Special Cases ◽  
The Many

To reason with existential rules (a.k.a. tuple-generating dependencies), one often computes universal models. Among the many such models of different structure and cardinality, the core is arguably the “best”. Especially for finitely satisfiable theories, where the core is the unique smallest universal model, it has advantages in query answering, non-monotonic reasoning, and data exchange. Unfortunately, computing cores is difficult and not supported by most reasoners. We therefore propose ways of computing cores using practically implemented methods from rule reasoning and answer set programming. Our focus is on cases where the standard chase algorithm produces a core. We characterise this desirable situation in general terms that apply to a large class of cores, derive concrete approaches for decidable special cases, and generalise these approaches to non-monotonic extensions of existential rules.

Some Fixpoint Techniques in Algebraic Structures and Applications to Computer Science

1987 ◽  
Vol 10 (4) ◽  
pp. 387-413
Author(s):  
Irène Guessarian
Keyword(s):  
Logic Programming ◽  
Computer Science ◽  
Proof Theory ◽  
Algebraic Structures ◽  
Data Bases

This paper recalls some fixpoint theorems in ordered algebraic structures and surveys some ways in which these theorems are applied in computer science. We describe via examples three main types of applications: in semantics and proof theory, in logic programming and in deductive data bases.

Objects in concurrent logic programming languages

1986 ◽  
Vol 21 (11) ◽  
pp. 242-257 ◽  
Author(s):  
Kenneth Kahn ◽  
Eric Dean Tribble ◽  
Mark S. Miller ◽  
Daniel G. Bobrow
Keyword(s):  
Logic Programming ◽  
Programming Languages ◽  
Concurrent Logic Programming ◽  
Logic Programming Languages
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