scholarly journals A Syntactic Operator for Forgetting that Satisfies Strong Persistence

2019 ◽  
Vol 19 (5-6) ◽  
pp. 1038-1055 ◽  
Author(s):  
MATTI BERTHOLD ◽  
RICARDO GONÇALVES ◽  
MATTHIAS KNORR ◽  
JOÃO LEITE
Keyword(s):  
Answer Set Programming ◽  
Abstract Characterization ◽  
Original Program ◽  
Answer Set

AbstractWhereas the operation of forgetting has recently seen a considerable amount of attention in the context of Answer Set Programming (ASP), most of it has focused on theoretical aspects, leaving the practical issues largely untouched. Recent studies include results about what sets of properties operators should satisfy, as well as the abstract characterization of several operators and their theoretical limits. However, no concrete operators have been investigated.In this paper, we address this issue by presenting the first concrete operator that satisfies strong persistence – a property that seems to best capture the essence of forgetting in the context of ASP – whenever this is possible, and many other important properties. The operator is syntactic, limiting the computation of the forgetting result to manipulating the rules in which the atoms to be forgotten occur, naturally yielding a forgetting result that is close to the original program.

scholarly journals When you must forget: Beyond strong persistence when forgetting in answer set programming

2017 ◽  
Vol 17 (5-6) ◽  
pp. 837-854
Author(s):  
RICARDO GONÇALVES ◽  
MATTHIAS KNORR ◽  
JOÃO LEITE ◽  
STEFAN WOLTRAN
Keyword(s):  
Computational Complexity ◽  
Answer Set Programming ◽  
Correct Result ◽  
Open Question ◽  
Shed Light ◽  
Answer Set

AbstractAmong the myriad of desirable properties discussed in the context of forgetting in Answer Set Programming, strong persistence naturally captures its essence. Recently, it has been shown that it is not always possible to forget a set of atoms from a program while obeying this property, and a precise criterion regarding what can be forgotten has been presented, accompanied by a class of forgetting operators that return the correct result when forgetting is possible. However, it is an open question what to do when we have to forget a set of atoms, but cannot without violating this property. In this paper, we address this issue and investigate three natural alternatives to forget when forgetting without violating strong persistence is not possible, which turn out to correspond to the different possible relaxations of the characterization of strong persistence. Additionally, we discuss their preferable usage, shed light on the relation between forgetting and notions of relativized equivalence established earlier in the context of Answer Set Programming, and present a detailed study on their computational complexity.

scholarly journals A general framework for equivalences in Answer-Set Programming by countermodels in the logic of Here-and-There

2011 ◽  
Vol 11 (2-3) ◽  
pp. 171-202 ◽  
Author(s):  
MICHAEL FINK
Keyword(s):  
General Framework ◽  
Answer Set Programming ◽  
Program Optimization ◽  
Logic Programs ◽  
Infinite Domains ◽  
General Semantics ◽  
Answer Set Semantics ◽  
Selection Of ◽  
Answer Set

AbstractDifferent notions of equivalence, such as the prominent notions of strong and uniform equivalence, have been studied in Answer-Set Programming, mainly for the purpose of identifying programs that can serve as substitutes without altering the semantics, for instance in program optimization. Such semantic comparisons are usually characterized by various selections of models in the logic of Here-and-There (HT). For uniform equivalence however, correct characterizations in terms of HT-models can only be obtained for finite theories, respectively programs. In this paper, we show that a selection of countermodels in HT captures uniform equivalence also for infinite theories. This result is turned into coherent characterizations of the different notions of equivalence by countermodels, as well as by a mixture of HT-models and countermodels (so-called equivalence interpretations). Moreover, we generalize the so-called notion of relativized hyperequivalence for programs to propositional theories, and apply the same methodology in order to obtain a semantic characterization which is amenable to infinite settings. This allows for a lifting of the results to first-order theories under a very general semantics given in terms of a quantified version of HT. We thus obtain a general framework for the study of various notions of equivalence for theories under answer-set semantics. Moreover, we prove an expedient property that allows for a simplified treatment of extended signatures, and provide further results for non-ground logic programs. In particular, uniform equivalence coincides under open and ordinary answer-set semantics, and for finite non-ground programs under these semantics, also the usual characterization of uniform equivalence in terms of maximal and total HT-models of the grounding is correct, even for infinite domains, when corresponding ground programs are infinite.

scholarly journals Applications of intuitionistic logic in Answer Set Programming

2004 ◽  
Vol 4 (3) ◽  
pp. 325-354 ◽  
Author(s):  
MAURICIO OSORIO ◽  
JUAN A. NAVARRO ◽  
JOSÉ ARRAZOLA
Keyword(s):  
Recent Result ◽  
Intuitionistic Logic ◽  
Answer Set Programming ◽  
Minimal Models ◽  
Logic Programs ◽  
Intermediate Logics ◽  
Answer Set Semantics ◽  
Answer Sets ◽  
Answer Set

We present some applications of intermediate logics in the field of Answer Set Programming (ASP). A brief, but comprehensive introduction to the answer set semantics, intuitionistic and other intermediate logics is given. Some equivalence notions and their applications are discussed. Some results on intermediate logics are shown, and applied later to prove properties of answer sets. A characterization of answer sets for logic programs with nested expressions is provided in terms of intuitionistic provability, generalizing a recent result given by Pearce. It is known that the answer set semantics for logic programs with nested expressions may select non-minimal models. Minimal models can be very important in some applications, therefore we studied them; in particular we obtain a characterization, in terms of intuitionistic logic, of answer sets which are also minimal models. We show that the logic G3 characterizes the notion of strong equivalence between programs under the semantic induced by these models. Finally we discuss possible applications and consequences of our results. They clearly state interesting links between ASP and intermediate logics, which might bring research in these two areas together.

scholarly journals Linear-Time Temporal Answer Set Programming

2021 ◽  
pp. 1-55
Author(s):  
FELICIDAD AGUADO ◽  
PEDRO CABALAR ◽  
MARTÍN DIÉGUEZ ◽  
GILBERTO PÉREZ ◽  
TORSTEN SCHAUB ◽  
...  
Keyword(s):  
Temporal Logic ◽  
Linear Time ◽  
Selection Criterion ◽  
Answer Set Programming ◽  
Logic Programs ◽  
Modal Operators ◽  
Linear Time Temporal Logic ◽  
Stable Models ◽  
Answer Set

Abstract In this survey, we present an overview on (Modal) Temporal Logic Programming in view of its application to Knowledge Representation and Declarative Problem Solving. The syntax of this extension of logic programs is the result of combining usual rules with temporal modal operators, as in Linear-time Temporal Logic (LTL). In the paper, we focus on the main recent results of the non-monotonic formalism called Temporal Equilibrium Logic (TEL) that is defined for the full syntax of LTL but involves a model selection criterion based on Equilibrium Logic, a well known logical characterization of Answer Set Programming (ASP). As a result, we obtain a proper extension of the stable models semantics for the general case of temporal formulas in the syntax of LTL. We recall the basic definitions for TEL and its monotonic basis, the temporal logic of Here-and-There (THT), and study the differences between finite and infinite trace length. We also provide further useful results, such as the translation into other formalisms like Quantified Equilibrium Logic and Second-order LTL, and some techniques for computing temporal stable models based on automata constructions. In the remainder of the paper, we focus on practical aspects, defining a syntactic fragment called (modal) temporal logic programs closer to ASP, and explaining how this has been exploited in the construction of the solver telingo, a temporal extension of the well-known ASP solver clingo that uses its incremental solving capabilities.

scholarly journals A Semantic Characterization ASP Base Revision

2019 ◽  
Vol 66 ◽  
pp. 989-1029
Author(s):  
Laurent Garcia ◽  
Claire Lefèvre ◽  
Igor Stéphan ◽  
Odile Papini ◽  
Éric Würbel
Keyword(s):  
Classical Logic ◽  
Answer Set Programming ◽  
Semantic Content ◽  
Logic Programs ◽  
Rule Based ◽  
Complexity Results ◽  
Base Revision ◽  
Answer Sets ◽  
Answer Set

The paper deals with base revision for Answer Set Programming (ASP). Base revision in classical logic is done by the removal of formulas. Exploiting the non-monotonicity of ASP allows one to propose other revision strategies, namely addition strategy or removal and/or addition strategy. These strategies allow one to define families of rule-based revision operators. The paper presents a semantic characterization of these families of revision operators in terms of answer sets. This semantic characterization allows for equivalently considering the evolution of syntactic logic programs and the evolution of their semantic content. It then studies the logical properties of the proposed operators and gives complexity results.  

A Constructive semantic characterization of aggregates in answer set programming

2007 ◽  
Vol 7 (3) ◽  
pp. 355-375 ◽  
Author(s):  
TRAN CAO SON ◽  
ENRICO PONTELLI
Keyword(s):  
Computational Complexity ◽  
Logic Programming ◽  
Answer Set Programming ◽  
Technical Note ◽  
Consequence Operator ◽  
The Cost ◽  
Answer Sets ◽  
Answer Set

AbstractThis technical note describes a monotone and continuous fixpoint operator to compute the answer sets of programs with aggregates. The fixpoint operator relies on the notion ofaggregate solution. Under certain conditions, this operator behaves identically to the three-valued immediate consequence operator ΦaggrPfor aggregate programs, independently proposed in Pelov (2004) and Pelovet al.(2004). This operator allows us to closely tie the computational complexity of the answer set checking and answer sets existence problems to the cost of checking a solution of the aggregates in the program. Finally, we relate the semantics described by the operator to other proposals for logic programming with aggregates.

scholarly journals About Epistemic Negation and World Views in Epistemic Logic Programs

2019 ◽  
Vol 19 (5-6) ◽  
pp. 790-807 ◽  
Author(s):  
STEFANIA COSTANTINI
Keyword(s):  
Epistemic Logic ◽  
Answer Set Programming ◽  
Logic Programs ◽  
World Views ◽  
Recent Approach ◽  
Answer Set

AbstractIn this paper we consider Epistemic Logic Programs, which extend Answer Set Programming (ASP) with “ epistemic operators” and “ epistemic negation”, and a recent approach to the semantics of such programs in terms ofWorld Views. We propose some observations on the existence and number of world views. We show how to exploit an extended ASP semantics in order to: (i) provide a characterization of world views, different from existing ones; (ii) query world views and query the whole set of world views.

scholarly journals On Uniform Equivalence of Epistemic Logic Programs

2019 ◽  
Vol 19 (5-6) ◽  
pp. 826-840
Author(s):  
WOLFGANG FABER ◽  
MICHAEL MORAK ◽  
STEFAN WOLTRAN
Keyword(s):  
Computational Complexity ◽  
Epistemic Logic ◽  
State Of The Art ◽  
Answer Set Programming ◽  
Polynomial Hierarchy ◽  
Logic Programs ◽  
The Third ◽  
New Research ◽  
Answer Set

AbstractEpistemic Logic Programs (ELPs) extend Answer Set Programming (ASP) with epistemic negation and have received renewed interest in recent years. This led to the development of new research and efficient solving systems for ELPs. In practice, ELPs are often written in a modular way, where each module interacts with other modules by accepting sets of facts as input, and passing on sets of facts as output. An interesting question then presents itself: under which conditions can such a module be replaced by another one without changing the outcome, for any set of input facts? This problem is known as uniform equivalence, and has been studied extensively for ASP. For ELPs, however, such an investigation is, as of yet, missing. In this paper, we therefore propose a characterization of uniform equivalence that can be directly applied to the language of state-of-the-art ELP solvers. We also investigate the computational complexity of deciding uniform equivalence for two ELPs, and show that it is on the third level of the polynomial hierarchy.

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