Answer Set Semantics Research Articles

Evaluating epistemic negation in answer set programming

Epistemic negation not along with default negation ¬ plays a key role in knowledge representation and nonmonotonic reasoning. However, the existing epistemic approaches such as those by Gelfond [13,15,14], Truszczynski [33] and Kahl et al. [18] behave not satisfactorily in that they suffer from the problems of unintended world views due to recursion through the epistemic modal operator K or M (KF and MF are shorthands for ¬notF and not¬F, respectively). In this paper we present a new approach to handling epistemic negation which is free of unintended world views and thus offers a solution to the long-standing problem of epistemic specifications which were introduced by Gelfond [13] over two decades ago. We consider general logic programs consisting of rules of the form H←B, where H and B are arbitrary first-order formulas possibly containing epistemic negation, and define a general epistemic answer set semantics for general logic programs by introducing a novel program transformation and a new definition of world views in which we apply epistemic negation to minimize the knowledge in world views. The general epistemic semantics is applicable to extend any existing answer set semantics, such as those defined in [26,27,32,1,8,12,29], with epistemic negation. For illustration, we extend FLP answer set semantics of Faber et al. [8] for general logic programs with epistemic negation, leading to epistemic FLP semantics. We also extend the more restrictive well-justified FLP semantics of Shen et al. [29], which is free of circularity for default negation, to an epistemic well-justified semantics. We consider the computational complexity of epistemic FLP semantics and show that for a propositional program Π with epistemic negation, deciding whether Π has epistemic FLP answer sets is Σ3p-complete and deciding whether a propositional formula F is true in Π under epistemic FLP semantics is Σ4p-complete in general, but has lower complexity for logic programs that match normal epistemic specifications, where the complexity of world view existence and query evaluation drops by one level in the polynomial hierarchy.

Mapping Action Language BC to Logic Programs: A Characterization by Postulates

We have earlier shown that the standard mappings from action languages B and C to logic programs under answer set semantics can be captured by sets of properties on transition systems. In this paper, we consider action language BC and show that a standard mapping from BC action descriptions to logic programs can be similarly captured when the action rules in the descriptions do not have consistency conditions.

Semi-equilibrium models for paracoherent answer set programs

The answer set semantics may assign a logic program to model, due to logical contradiction or unstable negation, which is caused by cyclic dependency of an atom on its negation. While logical contradictions can be handled with traditional techniques from paraconsistent reasoning, instability requires other methods. We consider resorting to a paracoherent semantics, in which 3-valued interpretations are used where a third truth value besides true and false expresses that an atom is believed true. This is at the basis of the semi-stable model semantics, which was defined using a program transformation. In this paper, we give a model-theoretic characterization of semi-stable models, which makes the semantics more accessible. Motivated by some anomalies of semi-stable model semantics with respect to basic epistemic properties, we propose an amendment that satisfies these properties. The latter has both a transformational and a model-theoretic characterization that reveals it as a relaxation of equilibrium logic, the logical reconstruction of answer set semantics, and is thus called the semi-equilibrium model semantics. We consider refinements of this semantics to respect modularity in the rules, based on splitting sets, the major tool for modularity in modeling and evaluating answer set programs. In that, we single out classes of canonical models that are amenable for customary bottom-up evaluation of answer set programs, with an option to switch to a paracoherent mode when lack of an answer set is detected. A complexity analysis of major reasoning tasks shows that semi-equilibrium models are harder than answer sets (i.e., equilibrium models), due to a global minimization step for keeping the gap between true and believed true atoms as small as possible. Our results contribute to the logical foundations of paracoherent answer set programming, which gains increasing importance in inconsistency management, and at the same time provide a basis for algorithm development and integration into answer set solvers.

Negation as a Resource: a Novel View on Answer Set Semantics*

In recent work, we provided a formulation of ASP programs in terms of linear logic theories. Based on this work, in this paper we propose and discuss a modified Answer Set Semantics, Resource-based Answer Set Semantics.

Defeasibility in answer set programs with defaults and argumentation rules

Defeasible reasoning has been studied extensively in the last two decades and many different and dissimilar approaches are currently on the table. This multitude of ideas has made the field hard to navigate and the different techniques hard to compare. Our earlier work on Logic Programming with Defaults and Argumentation Theories (LPDA) introduced a degree of unification into the approaches that rely on the well-founded semantics. The present work takes this idea further and introduces ASPDA (Answer Set Programs via Argumentation Rules) - a unifying framework for defeasibility of disjunctive logic programs under the Answer Set Programming (ASP). Since the well-founded and the answer set semantics underlie almost all existing approaches to defeasible reasoning in Logic Programming, LPDA and ASPDA together can be seen as an attempt to unify most of those approaches. In addition to ASPDA, we obtained a number of interesting and non-trivial results. First, we show that ASPDA is reducible to ordinary ASP programs. Second, we study reducibility of ASPDA to the non-disjunctive case and show that head-cycle-free ASPDA programs reduce to the non-disjunctive case - similarly to head-cycle-free ASP programs, but through a more complex transformation. We also shed light on the relationship between ASPDA and some of the earlier theories such as Defeasible Logic and LPDA.

FLP answer set semantics without circular justifications for general logic programs

The answer set semantics presented by Faber et al. [27] has been widely used to define so called FLP answer sets for different types of logic programs. However, it was recently observed that when being extended from normal to more general classes of logic programs, this approach may produce answer sets with circular justifications that are caused by self-supporting loops. The main reason for this behavior is that the FLP answer set semantics is not fully constructive by a bottom up construction of answer sets. In this paper, we overcome this problem by enhancing the FLP answer set semantics with a level mapping formalism such that every answer set I can be built by fixpoint iteration of a one-step provability operator (more precisely, an extended van Emden–Kowalski operator for the FLP reduct fΠI). This is inspired by the fact that under the standard answer set semantics, each answer set I of a normal logic program Π is obtainable by fixpoint iteration of the standard van Emden–Kowalski one-step provability operator for the Gelfond–Lifschitz reduct ΠI, which induces a level mapping. The enhanced FLP answer sets, which we call well-justified FLP answer sets, are thanks to the level mapping free of circular justifications. As a general framework, the well-justified FLP answer set semantics applies to logic programs with first-order formulas, logic programs with aggregates, description logic programs, hex-programs etc., provided that the rule satisfaction is properly extended to such general logic programs. We study in depth the computational complexity of FLP and well-justified FLP answer sets for general classes of logic programs. Our results show that the level mapping does not increase the worst-case complexity of FLP answer sets. Furthermore, we describe an implementation of the well-justified FLP answer set semantics, and report about an experimental evaluation, which indicates a potential for performance improvements by the level mapping in practice.

Formalizing Negotiations Using Logic Programming

The article introduces a logical framework for negotiation among dishonest agents. The framework relies on the use of abductive logic programming as a knowledge representation language for agents to deal with incomplete information and preferences. The article shows how intentionally false or inaccurate information of agents can be encoded in the agents' knowledge bases. Such disinformation can be effectively used in the process of negotiation to have desired outcomes by agents. The negotiation processes are formulated under the answer set semantics of abductive logic programming, and they enable the exploration of various strategies that agents can employ in their negotiation. A preliminary implementation has been developed using the ASP-Prolog platform.

Preferred First-Order Answer Set Programs

In this article, we consider the issue of how first-order answer set programs can be extended for handling preference reasoning. To this end, we propose a progression-based preference semantics for first-order answer set programs while explicit preference relations are presented. We study essential properties of the proposed preferred answer set semantics. To understand the expressiveness of preferred first-order answer set programming, we further specify a second-order logic representation which precisely characterizes the progression-based preference semantics.

Efficient HEX-Program Evaluation Based on Unfounded Sets

HEX-programs extend logic programs under the answer set semantics with external computations through external atoms. As reasoning from ground Horn programs with nonmonotonic external atoms of polynomial complexity is already on the second level of the polynomial hierarchy, minimality checking of answer set candidates needs special attention. To this end, we present an approach based on unfounded sets as a generalization of related techniques for ASP programs. The unfounded set detection is expressed as a propositional SAT problem, for which we provide two different encodings and optimizations to them. We then integrate our approach into a previously developed evaluation framework for HEX-programs, which is enriched by additional learning techniques that aim at avoiding the reconstruction of the same or related unfounded sets. Furthermore, we provide a syntactic criterion that allows one to skip the minimality check in many cases. An experimental evaluation shows that the new approach significantly decreases runtime.

Characterizing and extending answer set semantics using possibility theory

AbstractAnswer Set Programming (ASP) is a popular framework for modelling combinatorial problems. However, ASP cannot be used easily for reasoning about uncertain information. Possibilistic ASP (PASP) is an extension of ASP that combines possibilistic logic and ASP. In PASP a weight is associated with each rule, whereas this weight is interpreted as the certainty with which the conclusion can be established when the body is known to hold. As such, it allows us to model and reason about uncertain information in an intuitive way. In this paper we present new semantics for PASP in which rules are interpreted as constraints on possibility distributions. Special models of these constraints are then identified as possibilistic answer sets. In addition, since ASP is a special case of PASP in which all the rules are entirely certain, we obtain a new characterization of ASP in terms of constraints on possibility distributions. This allows us to uncover a new form of disjunction, called weak disjunction, that has not been previously considered in the literature. In addition to introducing and motivating the semantics of weak disjunction, we also pinpoint its computational complexity. In particular, while the complexity of most reasoning tasks coincides with standard disjunctive ASP, we find that brave reasoning for programs with weak disjunctions is easier.

I-ABM: combining institutional frameworks and agent-based modelling for the design of enforcement policies

Computer science advocates institutional frameworks as an effective tool for modelling policies and reasoning about their interplay. In practice, the rules or policies, of which the institutional framework consists, are often specified using a formal language, which allows for the full verification and validation of the framework (e.g. the consistency of policies) and the interplay between the policies and actors (e.g. violations). However, when modelling large-scale realistic systems, with numerous decision-making entities, scalability and complexity issues arise making it possible only to verify certain portions of the problem without reducing the scale. In the social sciences, agent-based modelling is a popular tool for analysing how entities interact within a system and react to the system properties. Agent-based modelling allows the specification of complex decision-making entities and experimentation with large numbers of different parameter sets for these entities in order to explore their effects on overall system performance. In this paper we describe how to achieve the best of both worlds, namely verification of a formal specification combined with the testing of large-scale systems with numerous different actor configurations. Hence, we offer an approach that allows for reasoning about policies, policy making and their consequences on a more comprehensive level than has been possible to date. We present the institutional agent-based model methodology to combine institutional frameworks with agent-based simulations). We furthermore present J-InstAL, a prototypical implementation of this methodology using the InstAL institutional framework whose specifications can be translated into a computational model under the answer set semantics, and an agent-based simulation based on the jason tool. Using a simplified contract enforcement example, we demonstrate the functionalities of this prototype and show how it can help to assess an appropriate fine level in case of contract violations.

A Model-Theoretic Approach to Belief Change in Answer Set Programming

We address the problem of belief change in (nonmonotonic) logic programming under answer set semantics. Our formal techniques are analogous to those of distance-based belief revision in propositional logic. In particular, we build upon the model theory of logic programs furnished by SE interpretations, where an SE interpretation is a model of a logic program in the same way that a classical interpretation is a model of a propositional formula. Hence we extend techniques from the area of belief revision based on distance between models to belief change in logic programs. We first consider belief revision: for logic programs P and Q , the goal is to determine a program R that corresponds to the revision of P by Q , denoted P * Q . We investigate several operators, including (logic program) expansion and two revision operators based on the distance between the SE models of logic programs. It proves to be the case that expansion is an interesting operator in its own right, unlike in classical belief revision where it is relatively uninteresting. Expansion and revision are shown to satisfy a suite of interesting properties; in particular, our revision operators satisfy all or nearly all of the AGM postulates for revision. We next consider approaches for merging a set of logic programs, P 1 , ..., P n . Again, our formal techniques are based on notions of relative distance between the SE models of the logic programs. Two approaches are examined. The first informally selects for each program P i those models of P i that vary the least from models of the other programs. The second approach informally selects those models of a program P 0 that are closest to the models of programs P 1 , ..., P n . In this case, P 0 can be thought of as a set of database integrity constraints. We examine these operators with regards to how they satisfy relevant postulate sets. Last, we present encodings for computing the revision as well as the merging of logic programs within the same logic programming framework. This gives rise to a direct implementation of our approach in terms of off-the-shelf answer set solvers. These encodings also reflect the fact that our change operators do not increase the complexity of the base formalism.

Some properties of system descriptions of

The paper discusses some properties of system descriptions in action language – a recent extension of action language (also known as ) by defined fluents. We give a sufficient condition guaranteeing that states of an system description are fully determined by statics and inertial fluents. In system descriptions satisfying this condition, defined fluents simply facilitate the description of dynamic domains; they are not essential and can be eliminated. We use our sufficient condition to identify a common core of action languages and . This is an expansion of the work of , who identified a common core of languages and . The results presented in this paper are based on the close relationship between action languages and the theory of logic programs under the answer set semantics.

On deductive bases for paraconsistent answer set semantics

It was proved by Odintsov and Pearce that the logic is a deductive base for paraconsistent answer set semantics (PAS) of logic programs with two kinds of negation. Here we describe the lattice of logics extending , characterise these logics via classes of -models, and prove that none of the proper extensions of is a deductive base for PAS.

Computing Loops with at Most One External Support Rule

A consequence of a logic program under answer set semantics is one that is true for all answer sets. This article considers using loop formulas to compute some of these consequences in order to increase the efficiency of answer set solvers. Since computing loop formulas are in general intractable, we consider only loops with either no external support or at most one external support, as their loop formulas are either unit or binary clauses. We show that for disjunctive logic programs, loop formulas of loops with no external support can be computed in polynomial time, and that an iterative procedure using unit propagation on these formulas and the program completion computes the well-founded models in the case of normal logic programs and the least fixed point of a simplification operator used by DLV for disjunctive logic programs. For loops with at most one external support, their loop formulas can be computed in polynomial time for normal logic programs, but are NP-hard for disjunctive programs. So for normal logic programs, we have a procedure similar to the iterative one for loops without any external support, but for disjunctive logic programs, we present a polynomial approximation algorithm. All these algorithms have been implemented, and our experiments show that for certain logic programs, the consequences computed by our algorithms can significantly speed up current ASP solvers cmodels, clasp, and DLV.

Dependency semantics for sequences of extended logic programs

In this work, we present a framework based on the notion of dependencies. We use this framework to define semantics for inconsistent belief bases in a modular way to define general tools for handling inconsistency. We consider belief bases represented by non-monotonic formalisms, and in particular use extended logic programs and belief bases represented by sequences of these. We show the presented frameworks appliance with the answer set semantics for consistent belief bases. Moreover, we define various instantiations of the framework and show relations to other approaches. We present ways to improve the resulting semantics by means of changes to modules of the framework that lead to the definition of improved approaches to conflict handling in logic programming-based knowledge bases.

Rough Description Logic Programs

The Semantic Web is an extension of the current World Wide Web, and aims to help computers to understand and process web information automatically. In recent years, the integration ontologies and rules has become a central topic in the Semantic Web. Therefore, many researchers have focused their study on investigating the combination of answer set programming with description logics for the semantic web. However, these can not deal with uncertainty and inexactness. To address this problem, we propose tightly coupled rough description logic programs (or simply rough dl-programs) under the answer set semantics, which can model uncertain, inexact information, and can deal with non monotonic reasoning at the same time. To our knowledge, this is the first such approach. First of all, we define the syntax and semantics of rough dl-program KB= ( L,P ), which is a tight integration of disjunctive logic program under the answer set semantics, rough set theory and rough description logic. Then, we present some reasoning problems of rough dl-program. Finally, we show some semantic properties of rough dl-program under the answer set semantics.

Tightly integrated probabilistic description logic programs for representing ontology mappings

Creating mappings between ontologies is a common way of approaching the semantic heterogeneity problem on the Semantic Web. To fit into the landscape of Semantic Web languages, a suitable, logic-based representation formalism for mappings is needed. We argue that such a formalism has to be able to deal with uncertainty and inconsistencies in automatically created mappings. We analyze the requirements for such a formalism, and we propose a novel approach to probabilistic description logic programs as such a formalism, which tightly combines normal logic programs under the well-founded semantics with both tractable ontology languages and Bayesian probabilities. We define the language, and we show that it can be used to resolve inconsistencies and merge mappings from different matchers based on the level of confidence assigned to different rules. Furthermore, we explore the semantic and computational aspects of probabilistic description logic programs under the well-founded semantics. In particular, we show that the well-founded semantics approximates the answer set semantics. We also describe algorithms for consistency checking and tight query processing, and we analyze the data and general complexity of these two central computational problems. As a crucial property, the novel tightly integrated probabilistic description logic programs under the well-founded semantics allow for tractable consistency checking and for tractable tight query processing in the data complexity, and they even have a first-order rewritable (and thus LogSpace data complexity) special case, which is especially interesting for representing ontology mappings.

The loop formula based semantics of description logic programs

Description logic programs (dl-programs) proposed by Eiter et al. constitute an elegant yet powerful formalism for the integration of answer set programming with description logics, for the Semantic Web. In this paper, we generalize the notions of completion and loop formulas of logic programs to description logic programs and show that the answer sets of a dl-program can be precisely captured by the models of its completion and loop formulas. Furthermore, we propose a new, alternative semantics for dl-programs, called the canonical answer set semantics, which is defined by the models of completion that satisfy what are called canonical loop formulas. A desirable property of canonical answer sets is that they are free of circular justifications. Some properties of canonical answer sets are also explored and we compare the canonical answer set semantics with the FLP-semantics and the answer set semantics by translating dl-programs into logic programs with abstract constraints. We present a clear picture on the relationship among these semantics variations for dl-programs.

Integrating Rules and Description Logics by Circumscription

We present a new approach to characterizing the semantics for the integration of rules and first-order logic in general, and description logics in particular, based on a circumscription characterization of answer set programming, introduced earlier by Lin and Zhou. We show that both Rosati's semantics based on NM-models and Lukasiewicz's answer set semantics can be characterized by circumscription, and the difference between the two can be seen as a matter of circumscription policies. This approach leads to a number of new insights. First, we rebut a criticism on Lukasiewicz's semantics for its inability to reason for negative consequences. Second, our approach leads to a spectrum of possible semantics based on different circumscription policies, and shows a clear picture of how they are related. Finally, we show that the idea of this paper can be applied to first-order general stable models.