scholarly journals A Denotational Semantics for Logic Programming

1985 ◽  
Vol 14 (201) ◽  
Author(s):  
Gudmund Skovbjerg Frandsen
Keyword(s):  
Logic Programming ◽  
Logic Program ◽  
Denotational Semantics ◽  
Power Domain ◽  
Fixpoint Semantics ◽  
Standard Domain

A fully abstract denotational semantics for logic programming has not been constructed yet. In this paper we present a denotational semantics that is almost fully abstract. We take the meaning of a logic program to be an element in a Plotkin power domain of substitutions. In this way our result shows that standard domain constructions suffice, when giving a semantics for logic programming. Using the well-known fixpoint semantics of logic programming we have to consider two different fixpoints in order to obtain information about both successful and failed computations. In contrast, our semantics is uniform in that the (single) meaning of a logic program contains information about both successful, failed and infinite computations. Finally, based on the full abstractness result, we argue that the detail level of substitutions is needed in any denotational semantics for logic programming.

A Roadmap on Updates

2009 ◽  
pp. 2261-2267
Author(s):  
Fernando Zacarías Flores ◽  
Dionicio Zacarías Flores ◽  
Rosalba Cuapa Canto ◽  
Luis Miguel Guzmán Muñoz
Keyword(s):  
Standard Model ◽  
Logic Programming ◽  
Structural Properties ◽  
Relational Databases ◽  
Logic Program ◽  
Answer Set Programming ◽  
Central Issue ◽  
The Standard Model ◽  
Answer Set

Updates, is a central issue in relational databases and knowledge databases. In the last years, it has been well studied in the non-monotonic reasoning paradigm. Several semantics for logic program updates have been proposed (Brewka, Dix, & Knonolige 1997), (De Schreye, Hermenegildo, & Pereira, 1999) (Katsumo & Mendelzon, 1991). However, recently a set of proposals has been characterized to propose mechanisms of updates based on logic and logic programming. All these mechanisms are built on semantics based on structural properties (Eiter, Fink, Sabattini & Thompits, 2000) (Leite, 2002) (Banti, Alferes & Brogi, 2003) (Zacarias, 2005). Furthermore, all these semantic ones coincide in considering the AGM proposal as the standard model in the update theory, for their wealth in properties. The AGM approach, introduced in (Alchourron, Gardenfors & Makinson, 1985) is the dominating paradigm in the area, but in the context of monotonic logic. All these proposals analyze and reinterpret the AGM postulates under the Answer Set Programming (ASP) such as (Eiter, Fink, Sabattini & Thompits, 2000). However, the majority of the adapted AGM and update postulates are violated by update programs, as shown in(De Schreye, Hermenegildo, & Pereira, 1999).

A Logic Programming Perspective on Rules

2010 ◽  
pp. 195-213
Author(s):  
Leon Sterling ◽  
Kuldar Taveter
Keyword(s):  
Logic Programming ◽  
Logic Program ◽  
Modelling And Simulation ◽  
Rule Based ◽  
Hybrid Computing ◽  
Rule Languages ◽  
The Web

Logic programming emerged from the realization that expressing knowledge in an appropriate clausal form in logic was akin to programming. The basic construct of a logic program can be viewed as a rule. This chapter will review rules from a logic programming perspective with an eye to developments within modern rule languages. It mentions rule interpreters, hybrid computing, interaction with the Web, and agents. An extended example is given concerning rule-based modelling and simulation of traffic at airports.

NESTED GUARDED HORN CLAUSES

1990 ◽  
Vol 01 (03) ◽  
pp. 249-263 ◽  
Author(s):  
MORENO FALASCHI ◽  
MAURIZIO GABBRIELLI ◽  
GIORGIO LEVI ◽  
MASAKI MURAKAMI
Keyword(s):  
Logic Programming ◽  
Operational Semantics ◽  
Horn Clauses ◽  
Fixpoint Semantics ◽  
New Feature ◽  
Definition Of

This paper defines a new concurrent logic language, Nested Guarded Horn Clauses (NGHC). The main new feature of the language is its concept of guard. In fact, an NGHC clause has several layers of (standard) guards. This syntactic innovation allows the definition of a complete (i.e. always applicable) set of unfolding rules and therefore of an unfolding semantics which is equivalent, with respect to the success set, to the operational semantics. A fixpoint semantics is also defined in the classic logic programming style and is proved equivalent to the unfolding one. Since it is possible to embed Flat GHC into NGHC, our method can be used to give a fixpoint semantics to FGHC as well.

scholarly journals Paracoherent Answer Set Semantics meets Argumentation Frameworks

2019 ◽  
Vol 19 (5-6) ◽  
pp. 688-704
Author(s):  
GIOVANNI AMENDOLA ◽  
FRANCESCO RICCA
Keyword(s):  
Logic Programming ◽  
Logic Program ◽  
Great Success ◽  
Argumentation Framework ◽  
Computational Costs ◽  
Abstract Argumentation ◽  
Answer Set Semantics ◽  
Answer Sets ◽  
Answer Set

AbstractIn the last years, abstract argumentation has met with great success in AI, since it has served to capture several non-monotonic logics for AI. Relations between argumentation framework (AF) semantics and logic programming ones are investigating more and more. In particular, great attention has been given to the well-known stable extensions of an AF, that are closely related to the answer sets of a logic program. However, if a framework admits a small incoherent part, no stable extension can be provided. To overcome this shortcoming, two semantics generalizing stable extensions have been studied, namely semi-stable and stage. In this paper, we show that another perspective is possible on incoherent AFs, called paracoherent extensions, as they have a counterpart in paracoherent answer set semantics. We compare this perspective with semi-stable and stage semantics, by showing that computational costs remain unchanged, and moreover an interesting symmetric behaviour is maintained.

scholarly journals Productive corecursion in logic programming

2017 ◽  
Vol 17 (5-6) ◽  
pp. 906-923 ◽  
Author(s):  
EKATERINA KOMENDANTSKAYA ◽  
YUE LI
Keyword(s):  
Data Structure ◽  
Logic Programming ◽  
State Of The Art ◽  
Logic Program ◽  
Stream Processing ◽  
The Internet ◽  
Logic Programs ◽  
Algorithmic Solution ◽  
Undecidable Property ◽  
Turing Complete

AbstractLogic Programming is a Turing complete language. As a consequence, designing algorithms that decide termination and non-termination of programs or decide inductive/coinductive soundness of formulae is a challenging task. For example, the existing state-of-the-art algorithms can only semi-decide coinductive soundness of queries in logic programming for regular formulae. Another, less famous, but equally fundamental and important undecidable property is productivity. If a derivation is infinite and coinductively sound, we may ask whether the computed answer it determines actually computes an infinite formula. If it does, the infinite computation is productive. This intuition was first expressed under the name of computations at infinity in the 80s. In modern days of the Internet and stream processing, its importance lies in connection to infinite data structure processing. Recently, an algorithm was presented that semi-decides a weaker property – of productivity of logic programs. A logic program is productive if it can give rise to productive derivations. In this paper, we strengthen these recent results. We propose a method that semi-decides productivity of individual derivations for regular formulae. Thus, we at last give an algorithmic counterpart to the notion of productivity of derivations in logic programming. This is the first algorithmic solution to the problem since it was raised more than 30 years ago. We also present an implementation of this algorithm.

DESIGN OF REDUNDANT FORMAL SPECIFICATIONS BY LOGIC PROGRAMMING: MERGING FORMAL TEXT AND GOOD COMMENTS

1994 ◽  
Vol 04 (03) ◽  
pp. 369-390
Author(s):  
SOPHIE RENAULT ◽  
PIERRE DERANSART
Keyword(s):  
Logic Programming ◽  
Formal Methods ◽  
Requirements Engineering ◽  
Design Method ◽  
Logic Program ◽  
Practical Experience ◽  
Formal Specifications ◽  
Promising Candidate ◽  
Rigorous Framework ◽  
Candidate Support

Among the various tasks involved in SE & KE, requirements engineering, specification, prototyping, and validation are regarded as crucial since they decide whether a software system fulfills the users’ expectations. Formal methods provide a rigorous framework to guaranteed. Logic Programming has been recently shown as a promising candidate support these tasks and some relevant features can be in that way captured and formally regarding these concerns. Nevertheless, formalism does need some explanation to let it be more readable and understandable. This paper focuses on a specification design method which mixes formal text (represented by a logic program) and comments (using either formal or informal assertions). By the design of a specification we refer to the intertwined tasks of describing the specification and improving it by the investigation of proofs. These proofs aim to verify the link between the specification and the comments, and are partly automated. Then we present our practical experience in the use of an interacti ve proof system. As an example, we show how this methodology is currently applied to the draft of standard Prolog.

scholarly journals Justifying answer sets using argumentation

2015 ◽  
Vol 16 (1) ◽  
pp. 59-110 ◽  
Author(s):  
CLAUDIA SCHULZ ◽  
FRANCESCA TONI
Keyword(s):  
Logic Programming ◽  
Logic Program ◽  
Argumentation Theory ◽  
Attack Tree ◽  
Attack Trees ◽  
Answer Sets ◽  
Answer Set

AbstractAn answer set is a plain set of literals which has no further structure that would explain why certain literals are part of it and why others are not. We show how argumentation theory can help to explain why a literal is or is not contained in a given answer set by defining two justification methods, both of which make use of the correspondence between answer sets of a logic program and stable extensions of the assumption-based argumentation (ABA) framework constructed from the same logic program.Attack Treesjustify a literal in argumentation-theoretic terms, i.e. using arguments and attacks between them, whereasABA-Based Answer Set Justificationsexpress the same justification structure in logic programming terms, that is using literals and their relationships. Interestingly, an ABA-Based Answer Set Justification corresponds to an admissible fragment of the answer set in question, and an Attack Tree corresponds to an admissible fragment of the stable extension corresponding to this answer set.

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