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

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.

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

10.1017/s1471068420000253 ◽

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 ◽

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.

Paracoherent Answer Set Semantics meets Argumentation Frameworks

10.1017/s1471068419000139 ◽

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.

Reasoning with Inconsistent Possibilistic Ontologies by Applying Argument Accrual

Journal of Computer Science and Technology ◽

10.24215/16666038.17.e16 ◽

2017 ◽

Vol 17 (02) ◽

pp. e16

Author(s):

Sergio Alejandro Gómez

Keyword(s):

Logic Programming ◽

Description Logic ◽

Logic Programs ◽

Argumentation Framework ◽

Abstract Argumentation ◽

Possibilistic Logic ◽

Grounded Semantics

We present an approach for performing instance checking in possibilistic description logic programming ontologies by accruing arguments that support the membership of individuals to concepts. Ontologies are interpreted as possibilistic logic programs where accruals of arguments as regarded as vertexes in an abstract argumentation framework. A suitable attack relation between accruals is defined. We present a reasoning framework with a case study and a Java-based implementation for enacting the proposed approach that is capable of reasoning under Dung’s grounded semantics.

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

10.1017/s1471068405002589 ◽

2006 ◽

Vol 6 (1-2) ◽

pp. 169-212 ◽

Cited By ~ 14

Author(s):

STEFANIA COSTANTINI

Keyword(s):

Canonical Form ◽

Logic Program ◽

Practical Importance ◽

The Body ◽

Fundamental Result ◽

Stable Model ◽

Logic Programs ◽

Truth Value ◽

Answer Sets ◽

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.

Preferred extensions as stable models

10.1017/s1471068408003359 ◽

2008 ◽

Vol 8 (04) ◽

pp. 527-543 ◽

Cited By ~ 27

Author(s):

JUAN CARLOS NIEVES ◽

ULISES CORTÉS ◽

MAURICIO OSORIO

Keyword(s):

Direct Relationship ◽

Logic Program ◽

Nonmonotonic Reasoning ◽

Mapping Function ◽

Propositional Formula ◽

Stable Model ◽

Minimal Models ◽

Argumentation Framework ◽

Polynomial Size ◽

AbstractGiven an argumentation frameworkAF, we introduce a mapping function that constructs a disjunctive logic programP, such that the preferred extensions ofAFcorrespond to the stable models ofP, after intersecting each stable model with the relevant atoms. The given mapping function is of polynomial size w.r.t.AF.In particular, we identify that there is a direct relationship between the minimal models of a propositional formula and the preferred extensions of an argumentation framework by working on representing the defeated arguments. Then we show how to infer the preferred extensions of an argumentation framework by using UNSAT algorithms and disjunctive stable model solvers. The relevance of this result is that we define a direct relationship between one of the most satisfactory argumentation semantics and one of the most successful approach of nonmonotonic reasoning i.e., logic programming with the stable model semantics.

On the Semantics of Logic Programs with Preferences

Journal of Artificial Intelligence Research ◽

10.1613/jair.2371 ◽

2007 ◽

Vol 30 ◽

pp. 501-523 ◽

Cited By ~ 4

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 ◽

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.

On the Equivalence Between Abstract Dialectical Frameworks and Logic Programs

10.1017/s1471068419000280 ◽

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 ◽

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.

Temporal logic programs with variables

10.1017/s1471068416000570 ◽

2016 ◽

Vol 17 (2) ◽

pp. 226-243 ◽

Cited By ~ 1

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.

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

Journal of Artificial Intelligence Research ◽

10.1613/jair.1.11408 ◽

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 ◽

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.

Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence ◽

Forgetting Auxiliary Atoms in Forks (Extended Abstract)

10.24963/ijcai.2020/696 ◽

2020 ◽

Author(s):

Felicidad Aguado ◽

Pedro Cabalar ◽

Jorge Fandinno ◽

David Pearce ◽

Gilberto Pérez ◽

...

Keyword(s):

Logic Program ◽

Logic Programs ◽

Conservative Extension ◽

External Context ◽

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.