scholarly journals Default Negation as Explicit Negation plus Update

2021 ◽  
Vol 27 (1) ◽  
pp. 64-81
Author(s):  
Reinhard Kahle
Keyword(s):  
Logic Programming ◽  
Dynamic Logic ◽  
Stable Model ◽  
Normal Logic ◽  
Explicit Negation

 We argue that under the stable model semantics default negation can be read as explicit negation with update. We show that dynamic logic programming which is based on default negation, even in the heads, can be interpreted in a variant of updates with explicit negation only. As corollaries, we get an easy description of default negation in generalized and normal logic programming where initially negated literals are updated. These results are discussed with respect to the understanding of negation in logic.

scholarly journals Interdefinability of defeasible logic and logic programming under the well-founded semantics

2011 ◽  
Vol 13 (1) ◽  
pp. 107-142 ◽  
Author(s):  
FREDERICK MAIER
Keyword(s):  
Logic Programming ◽  
Opposite Direction ◽  
Stable Model ◽  
Logic Programs ◽  
Defeasible Logic ◽  
Normal Logic

AbstractWe provide a method of translating theories of Nute's defeasible logic into logic programs, and a corresponding translation in the opposite direction. Under certain natural restrictions, the conclusions of defeasible theories under the ambiguity propagating defeasible logic ADL correspond to those of the well-founded semantics for normal logic programs, and so it turns out that the two formalisms are closely related. Using the same translation of logic programs into defeasible theories, the semantics for the ambiguity blocking defeasible logic NDL can be seen as indirectly providing an ambiguity blocking semantics for logic programs. We also provide antimonotone operators for both ADL and NDL, each based on the Gelfond–Lifschitz (GL) operator for logic programs. For defeasible theories without defeaters or priorities on rules, the operator for ADL corresponds to the GL operator and so can be seen as partially capturing the consequences according to ADL. Similarly, the operator for NDL captures the consequences according to NDL, though in this case no restrictions on theories apply. Both operators can be used to define stable model semantics for defeasible theories.

scholarly journals Deriving conclusions from non-monotonic cause-effect relations

2016 ◽  
Vol 16 (5-6) ◽  
pp. 670-687 ◽  
Author(s):  
JORGE FANDINNO
Keyword(s):  
Knowledge Representation ◽  
Logic Programming ◽  
Causal Effect ◽  
Stable Model ◽  
Logic Programs ◽  
Causal Relations ◽  
Initial Approach ◽  
Sufficient Cause ◽  
Different Types ◽  
Normal Logic

AbstractWe present an extension of Logic Programming (under stable models semantics) that, not only allows concluding whether a true atom is a cause of another atom, but alsoderiving new conclusionsfrom these causal-effect relations. This is expressive enough to capture informal rules like “if some agent's actionshave beennecessaryto cause an eventEthen conclude atomcaused(,E),” something that, to the best of our knowledge, had not been formalised in the literature. To this aim, we start from a first attempt that proposed extending the syntax of logic programs with so-calledcausal literals. These causal literals are expressions that can be used in rule bodies and allow inspecting the derivation of some atomAin the program with respect to some query function ψ. Depending on how these query functions are defined, we can model different types of causal relations such as sufficient, necessary or contributory causes, for instance. The initial approach was specifically focused on monotonic query functions. This was enough to cover sufficient cause-effect relations but, unfortunately, necessary and contributory are essentiallynon-monotonic. In this work, we define a semantics for non-monotonic causal literals showing that, not only extends the stable model semantics for normal logic programs, but also preserves many of its usual desirable properties for the extended syntax. Using this new semantics, we provide precise definitions ofnecessaryandcontributorycausal relations and briefly explain their behaviour on a pair of typical examples from the Knowledge Representation literature.

scholarly journals Order-consistent programs are cautiously monotonic

2001 ◽  
Vol 1 (4) ◽  
pp. 487-495 ◽  
Author(s):  
HUDSON TURNER
Keyword(s):  
Stable Model ◽  
Logic Programs ◽  
Normal Logic ◽  
Answer Sets ◽  
Answer Set

Some normal logic programs under the answer set (or stable model) semantics lack the appealing property of ‘cautious monotonicity.’ That is, augmenting a program with one of its consequences may cause it to lose another of its consequences. The syntactic condition of ‘order-consistency’ was shown by Fages to guarantee existence of an answer set. This note establishes that order-consistent programs are not only consistent, but cautiously monotonic. From this it follows that they are also ‘cumulative’. That is, augmenting an order-consistent program with some of its consequences does not alter its consequences. In fact, as we show, its answer sets remain unchanged.

scholarly journals A Case for Query-driven Predicate Answer Set Programming

10.29007/ngm2 ◽  
2018 ◽  
Author(s):  
Gopal Gupta ◽  
Elmer Salazar ◽  
Kyle Marple ◽  
Zhuo Chen ◽  
Farhad Shakerin
Keyword(s):  
Logic Programming ◽  
Common Sense ◽  
Automated Reasoning ◽  
Answer Set Programming ◽  
Stable Model ◽  
Common Sense Reasoning ◽  
Knowledge Based ◽  
Full Power ◽  
Programming Systems ◽  
Answer Set

Answer Set Programming (ASP) has emerged as a successful paradigm for developing intelligent applications. ASP is based on adding negation as failure to logic programming under the stable model semantics regime. ASP allows for sophisticated reasoning mechanisms that are employed by humans to be modeled elegantly. We argue that being able to model common sense reasoning as used by humans is critical for success of automated reasoning. We also argue that extending answer programming systems to general predicates is critical to realizing the full power of ASP. Goal-directed predicate ASP systems are needed to make the ASP technology practical for building large, scalable knowledge-based applications.

scholarly journals A Functorial Framework for Constraint Normal Logic Programming

2006 ◽  
pp. 555-577 ◽  
Author(s):  
Paqui Lucio ◽  
Fernando Orejas ◽  
Edelmira Pasarella ◽  
Elvira Pino
Keyword(s):  
Logic Programming ◽  
Normal Logic

scholarly journals Logic programming with social features

2008 ◽  
Vol 8 (5-6) ◽  
pp. 643-690 ◽  
Author(s):  
FRANCESCO BUCCAFURRI ◽  
GIANLUCA CAMINITI
Keyword(s):  
Logic Programming ◽  
Everyday Life ◽  
Mental State ◽  
Mental States ◽  
Stable Model ◽  
Logic Programs ◽  
Social Features ◽  
Knowledge Representation Language ◽  
Representation Language ◽  
Semantics Of Logic Programs

AbstractIn everyday life it happens that a person has to reason out 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 behavior by reasoning about the others' mental state. In this paper we focus on a knowledge-representation language derived from logic programming which both supports the representation of mental states of individual communities and provides each with the capability of reasoning about others' mental states and acting accordingly. The proposed semantics is shown to be translatable into stable model semantics of logic programs with aggregates.

scholarly journals Relating defeasible and normal logic programming through transformation properties

2003 ◽  
Vol 290 (1) ◽  
pp. 499-529 ◽  
Author(s):  
Carlos Iván Chesñevar ◽  
Jürgen Dix ◽  
Frieder Stolzenburg ◽  
G.R.Guillermo Ricardo Simari
Keyword(s):  
Logic Programming ◽  
Normal Logic
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