scholarly journals Polynomial and Exponential Bounded Logic Programs with Function Symbols: Some New Decidable Classes

2019 ◽  
Vol 64 ◽  
pp. 749-815
Author(s):  
Vernon Asuncion ◽  
Yan Zhang ◽  
Heng Zhang ◽  
Ruixuan Li
Keyword(s):  
Propositional Logic ◽  
Logic Program ◽  
Logic Programs ◽  
Decidable Classes ◽  
Stable Models

A logic program with function symbols is called finitely ground if there is a finite propositional logic program whose stable models are exactly the same as the stable models of this program. Finite groundability is an important property for logic programs with function symbols because it makes feasible to compute such programs' stable models using traditional ASP solvers. In this paper, we introduce new decidable classes of finitely ground programs called poly-bounded and k-EXP-bounded programs, which, to the best of our knowledge, strictly contain all other decidable classes of finitely ground programs discovered so far in the literature. We also study the relevant complexity properties for these classes of programs. We prove that the membership complexities for poly-bounded and k-EXP-bounded programs are EXPTIME-complete and (k+1)-EXPTIME-complete, respectively.

scholarly journals Defining the Semantics of Abstract Argumentation Frameworks through Logic Programs and Partial Stable Models (Extended Abstract)

2021 ◽  
Author(s):  
Gianvincenzo Alfano ◽  
Sergio Greco ◽  
Francesco Parisi ◽  
Irina Trubitsyna
Keyword(s):  
Logic Program ◽  
Logic Programs ◽  
Argumentation Framework ◽  
Abstract Argumentation ◽  
Stable Models

Extensions of Dung’s Argumentation Framework (AF) include the class of Recursive Bipolar AFs (Rec-BAFs), i.e. AFs with recursive attacks and supports. We show that a Rec-BAF \Delta can be translated into a logic program P_\Delta so that the extensions of \Delta under different semantics coincide with subsets of the partial stable models of P_\Delta.

scholarly journals On the existence of stable models of non-stratified logic programs

2006 ◽  
Vol 6 (1-2) ◽  
pp. 169-212 ◽  
Author(s):  
STEFANIA COSTANTINI
Keyword(s):  
Canonical Form ◽  
Logic Program ◽  
Practical Importance ◽  
The Body ◽  
Fundamental Result ◽  
Stable Model ◽  
Logic Programs ◽  
Truth Value ◽  
Answer Sets ◽  
Stable Models

In this paper we analyze the relationship between cyclic definitions and consistency in Gelfond-Lifschitz's answer sets semantics (originally defined as ‘stable model semantics’). This paper introduces a fundamental result, which is relevant for Answer Set programming, and planning. For the first time since the definition of the stable model semantics, the class of logic programs for which a stable model exists is given a syntactic characterization. This condition may have a practical importance both for defining new algorithms for checking consistency and computing answer sets, and for improving the existing systems. The approach of this paper is to introduce a new canonical form (to which any logic program can be reduced to), to focus the attention on cyclic dependencies. The technical result is then given in terms of programs in canonical form (canonical programs), without loss of generality: the stable models of any general logic program coincide (up to the language) to those of the corresponding canonical program. The result is based on identifying the cycles contained in the program, showing that stable models of the overall program are composed of stable models of suitable sub-programs, corresponding to the cycles, and on defining the Cycle Graph. Each vertex of this graph corresponds to one cycle, and each edge corresponds to one handle, which is a literal containing an atom that, occurring in both cycles, actually determines a connection between them. In fact, the truth value of the handle in the cycle where it appears as the head of a rule, influences the truth value of the atoms of the cycle(s) where it occurs in the body. We can therefore introduce the concept of a handle path, connecting different cycles. Cycles can be even, if they consist of an even number of rules, or vice versa they can be odd. Problems for consistency, as it is well-known, originate in the odd cycles. If for every odd cycle we can find a handle path with certain properties, then the existence of stable model is guaranteed. We will show that based on this results new classes of consistent programs can be defined, and that cycles and cycle graphs can be generalized to components and component graphs.

scholarly journals On the Semantics of Logic Programs with Preferences

2007 ◽  
Vol 30 ◽  
pp. 501-523 ◽  
Author(s):  
S. Greco ◽  
I. Trubitsyna ◽  
E. Zumpano
Keyword(s):  
Logic Programming ◽  
Complexity Analysis ◽  
Structural Information ◽  
Logic Program ◽  
Set Optimization ◽  
Logic Programs ◽  
Preference Relations ◽  
New Interpretation ◽  
Semantics Of Logic Programs ◽  
Stable Models

This work is a contribution to prioritized reasoning in logic programming in the presence of preference relations involving atoms. The technique, providing a new interpretation for prioritized logic programs, is inspired by the semantics of Prioritized Logic Programming and enriched with the use of structural information of preference of Answer Set Optimization Programming. Specifically, the analysis of the logic program is carried out together with the analysis of preferences in order to determine the choice order and the sets of comparable models. The new semantics is compared with other approaches known in the literature and complexity analysis is also performed, showing that, with respect to other similar approaches previously proposed, the complexity of computing preferred stable models does not increase.

scholarly journals On the Equivalence Between Abstract Dialectical Frameworks and Logic Programs

2019 ◽  
Vol 19 (5-6) ◽  
pp. 941-956
Author(s):  
JOÃO ALCÂNTARA ◽  
SAMY SÁ ◽  
JUAN ACOSTA-GUADARRAMA
Keyword(s):  
Logic Program ◽  
Logic Programs ◽  
Different Types ◽  
Stable Semantics ◽  
Acceptance Condition ◽  
Normal Logic ◽  
Normal Logic Program ◽  
Stable Models

AbstractAbstract Dialectical Frameworks (ADFs) are argumentation frameworks where each node is associated with an acceptance condition. This allows us to model different types of dependencies as supports and attacks. Previous studies provided a translation from Normal Logic Programs (NLPs) to ADFs and proved the stable models semantics for a normal logic program has an equivalent semantics to that of the corresponding ADF. However, these studies failed in identifying a semantics for ADFs equivalent to a three-valued semantics (as partial stable models and well-founded models) for NLPs. In this work, we focus on a fragment of ADFs, called Attacking Dialectical Frameworks (ADF+s), and provide a translation from NLPs to ADF+s robust enough to guarantee the equivalence between partial stable models, well-founded models, regular models, stable models semantics for NLPs and respectively complete models, grounded models, preferred models, stable models for ADFs. In addition, we define a new semantics for ADF+s, called L-stable, and show it is equivalent to the L-stable semantics for NLPs.

scholarly journals Temporal logic programs with variables

2016 ◽  
Vol 17 (2) ◽  
pp. 226-243 ◽  
Author(s):  
FELICIDAD AGUADO ◽  
PEDRO CABALAR ◽  
GILBERTO PÉREZ ◽  
CONCEPCIÓN VIDAL ◽  
MARTÍN DIÉGUEZ
Keyword(s):  
Temporal Logic ◽  
Linear Time ◽  
Logic Program ◽  
Answer Set Programming ◽  
Logic Programs ◽  
First Order ◽  
Linear Time Temporal Logic ◽  
Definition Of ◽  
Stable Models ◽  
Answer Set

AbstractIn this note, we consider the problem of introducing variables in temporal logic programs under the formalism of Temporal Equilibrium Logic, an extension of Answer Set Programming for dealing with linear-time modal operators. To this aim, we provide a definition of a first-order version of Temporal Equilibrium Logic that shares the syntax of first-order Linear-time Temporal Logic but has different semantics, selecting some Linear-time Temporal Logic models we call temporal stable models. Then, we consider a subclass of theories (called splittable temporal logic programs) that are close to usual logic programs but allowing a restricted use of temporal operators. In this setting, we provide a syntactic definition of safe variables that suffices to show the property of domain independence – that is, addition of arbitrary elements in the universe does not vary the set of temporal stable models. Finally, we present a method for computing the derivable facts by constructing a non-temporal logic program with variables that is fed to a standard Answer Set Programming grounder. The information provided by the grounder is then used to generate a subset of ground temporal rules which is equivalent to (and generally smaller than) the full program instantiation.

scholarly journals On the Semantics of Abstract Argumentation Frameworks: A Logic Programming Approach

2020 ◽  
Vol 20 (5) ◽  
pp. 703-718
Author(s):  
Gianvincenzo Alfano ◽  
Sergio Greco ◽  
Francesco Parisi ◽  
Irina Trubitsyna
Keyword(s):  
Logic Programming ◽  
Logic Program ◽  
Programming Approach ◽  
Logic Programs ◽  
Argumentation Framework ◽  
Abstract Argumentation ◽  
Stable Models

AbstractRecently there has been an increasing interest in frameworks extending Dung’s abstract Argumentation Framework (AF). Popular extensions include bipolar AFs and AFs with recursive attacks and necessary supports. Although the relationships between AF semantics and Partial Stable Models (PSMs) of logic programs has been deeply investigated, this is not the case for more general frameworks extending AF.In this paper we explore the relationships between AF-based frameworks and PSMs. We show that every AF-based framework Δ can be translated into a logic program PΔ so that the extensions prescribed by different semantics of Δ coincide with subsets of the PSMs of PΔ. We provide a logic programming approach that characterizes, in an elegant and uniform way, the semantics of several AF-based frameworks. This result allows also to define the semantics for new AF-based frameworks, such as AFs with recursive attacks and recursive deductive supports.

scholarly journals Forgetting Auxiliary Atoms in Forks (Extended Abstract)

2020 ◽  
Author(s):  
Felicidad Aguado ◽  
Pedro Cabalar ◽  
Jorge Fandinno ◽  
David Pearce ◽  
Gilberto Pérez ◽  
...  
Keyword(s):  
Logic Program ◽  
Logic Programs ◽  
Conservative Extension ◽  
External Context ◽  
Stable Models

This work tackles the problem of checking strong equivalence of logic programs that may contain local auxiliary atoms, to be removed from their stable models and to be forbidden in any external context. We call this property projective strong equivalence (PSE). It has been recently proved that not any logic program containing auxiliary atoms can be reformulated, under PSE, as another logic program or formula without them -- this is known as strongly persistent forgetting. In this paper, we introduce a conservative extension of Equilibrium Logic and its monotonic basis, the logic of Here-and-There, in which we deal with a new connective we call fork. We provide a semantic characterisation of PSE for forks and use it to show that, in this extension, it is always possible to forget auxiliary atoms under strong persistence. We further define when the obtained fork is representable as a regular formula.

Well-Founded Semantics Coincides with Three-Valued Stable Semantics1

1990 ◽  
Vol 13 (4) ◽  
pp. 445-463
Author(s):  
Teodor Przymusinski
Keyword(s):  
Logic Program ◽  
Natural Extension ◽  
Natural Generalization ◽  
Stable Model ◽  
Logic Programs ◽  
Default Theory ◽  
Recent Approach ◽  
Stable Semantics ◽  
Disjunctive Logic Programs ◽  
Stable Models

We introduce 3-valued stable models which are a natural generalization of standard (2-valued) stable models. We show that every logic program P has at least one 3-valued stable model and that the well-founded model of any program P [Van Gelder et al., 1990] coincides with the smallest 3-valued stable model of P. We conclude that the well-founded semantics of an arbitrary logic program coincides with the 3-valued stable model semantics. The 3-valued stable semantics is closely related to non-monotonic formalisms in AI. Namely, every program P can be translated into a suitable autoepistemic (resp. default) theory P ˆ so that the 3-valued stable semantics of P coincides with the (3-valued) autoepistemic (resp. default) semantics of P ˆ. Similar results hold for circumscription and CWA. Moreover, it can be shown that the 3-valued stable semantics has a natural extension to the class of all disjunctive logic programs and deductive databases. Finally, following upon the recent approach developed by Gelfond and Lifschitz, we extend all of our results to more general logic programs which, in addition to the use of negation as failure, permit the use of classical negation.

Y-Logic: A Framework for Reasoning About Chameleonic Programs with Inconsistent Completions

1990 ◽  
Vol 13 (4) ◽  
pp. 465-483
Author(s):  
V.S. Subrahmanian
Keyword(s):  
Classical Logic ◽  
Logic Program ◽  
Logic Programs ◽  
Large Subset ◽  
General Logic ◽  
Traditional Sense

Large logic programs are normally designed by teams of individuals, each of whom designs a subprogram. While each of these subprograms may have consistent completions, the logic program obtained by taking the union of these subprograms may not. However, the resulting program still serves a useful purpose, for a (possibly) very large subset of it still has a consistent completion. We argue that “small” inconsistencies may cause a logic program to have no models (in the traditional sense), even though it still serves some useful purpose. A semantics is developed in this paper for general logic programs which ascribes a very reasonable meaning to general logic programs irrespective of whether they have consistent (in the classical logic sense) completions.

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