scholarly journals Stable models for infinitary formulas with extensional atoms

2016 ◽  
Vol 16 (5-6) ◽  
pp. 771-786
Author(s):  
AMELIA HARRISON ◽  
VLADIMIR LIFSCHITZ
Keyword(s):  
Programming Languages ◽  
Answer Set Programming ◽  
Splitting Theorem ◽  
First Order ◽  
Definition Of ◽  
Stable Models ◽  
Answer Set

AbstractThe definition of stable models for propositional formulas with infinite conjunctions and disjunctions can be used to describe the semantics of answer set programming languages. In this note, we enhance that definition by introducing a distinction between intensional and extensional atoms. The symmetric splitting theorem for first-order formulas is then extended to infinitary formulas and used to reason about infinitary definitions.

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 Module theorem for the general theory of stable models

2012 ◽  
Vol 12 (4-5) ◽  
pp. 719-735 ◽  
Author(s):  
JOSEPH BABB ◽  
JOOHYUNG LEE
Keyword(s):  
General Theory ◽  
General Class ◽  
Answer Set Programming ◽  
Splitting Theorem ◽  
Logic Programs ◽  
Input Output ◽  
Answer Sets ◽  
Output Interface ◽  
Stable Models ◽  
Answer Set

AbstractThe module theorem by Janhunen et al. demonstrates how to provide a modular structure in answer set programming, where each module has a well-defined input/output interface which can be used to establish the compositionality of answer sets. The theorem is useful in the analysis of answer set programs, and is a basis of incremental grounding and reactive answer set programming. We extend the module theorem to the general theory of stable models by Ferraris et al. The generalization applies to non-ground logic programs allowing useful constructs in answer set programming, such as choice rules, the count aggregate, and nested expressions. Our extension is based on relating the module theorem to the symmetric splitting theorem by Ferraris et al. Based on this result, we reformulate and extend the theory of incremental answer set computation to a more general class of programs.

scholarly journals Relating Two Dialects of Answer Set Programming

2019 ◽  
Vol 19 (5-6) ◽  
pp. 1006-1020 ◽  
Author(s):  
AMELIA HARRISON ◽  
VLADIMIR LIFSCHITZ
Keyword(s):  
Working Group ◽  
Answer Set Programming ◽  
Stable Model ◽  
Input Language ◽  
Core Language ◽  
Definition Of ◽  
Stable Models ◽  
Answer Set

AbstractThe input language of the answer set solver clingo is based on the definition of a stable model proposed by Paolo Ferraris. The semantics of the ASP-Core language, developed by the ASP Standardization Working Group, uses the approach to stable models due to Wolfgang Faber, Nicola Leone, and Gerald Pfeifer. The two languages are based on different versions of the stable model semantics, and the ASP-Core document requires, “for the sake of an uncontroversial semantics,” that programs avoid the use of recursion through aggregates. In this paper we prove that the absence of recursion through aggregates does indeed guarantee the equivalence between the two versions of the stable model semantics, and show how that requirement can be relaxed without violating the equivalence property.

scholarly journals Here and There with Arithmetic

2021 ◽  
pp. 1-15
Author(s):  
VLADIMIR LIFSCHITZ
Keyword(s):  
Programming Language ◽  
Propositional Logic ◽  
Answer Set Programming ◽  
The Other ◽  
Arithmetic Operations ◽  
First Order ◽  
The Relationship ◽  
Answer Set

Abstarct In the theory of answer set programming, two groups of rules are called strongly equivalent if, informally speaking, they have the same meaning in any context. The relationship between strong equivalence and the propositional logic of here-and-there allows us to establish strong equivalence by deriving rules of each group from rules of the other. In the process, rules are rewritten as propositional formulas. We extend this method of proving strong equivalence to an answer set programming language that includes operations on integers. The formula representing a rule in this language is a first-order formula that may contain comparison symbols among its predicate constants, and symbols for arithmetic operations among its function constants. The paper is under consideration for acceptance in TPLP.

Program completion in the input language of GRINGO

2017 ◽  
Vol 17 (5-6) ◽  
pp. 855-871 ◽  
Author(s):  
AMELIA HARRISON ◽  
VLADIMIR LIFSCHITZ ◽  
DHANANJAY RAJU
Keyword(s):  
Reverse Engineering ◽  
Large Class ◽  
Logic Program ◽  
Answer Set Programming ◽  
Program Completion ◽  
Engineering Process ◽  
Input Language ◽  
Definition Of ◽  
Answer Set

AbstractWe argue that turning a logic program into a set of completed definitions can be sometimes thought of as the “reverse engineering” process of generating a set of conditions that could serve as a specification for it. Accordingly, it may be useful to define completion for a large class of Answer Set Programming (ASP) programs and to automate the process of generating and simplifying completion formulas. Examining the output produced by this kind of software may help programmers to see more clearly what their program does, and to what degree its behavior conforms with their expectations. As a step toward this goal, we propose here a definition of program completion for a large class of programs in the input language of the ASP grounder gringo, and study its properties.

STRATEGIES TO DEFEND A PROTAGONIST OF AN EVENT

2010 ◽  
Vol 19 (04) ◽  
pp. 439-464
Author(s):  
SARA BOUTOUHAMI ◽  
DANIEL KAYSER
Keyword(s):  
Natural Language ◽  
Experimental Validation ◽  
Answer Set Programming ◽  
First Order ◽  
Starting Point ◽  
First Results ◽  
Argumentative Strategies ◽  
Complete Set ◽  
Car Accident ◽  
Answer Set

We aim at controlling the biases that exist in every description, in order to give the best possible image of one of the protagonists of an event. Starting from a supposedly complete set of propositions accounting for an event, we develop various argumentative strategies (insinuation, justification, reference to customary norms) to imply the facts that cannot be simply omitted but have the "wrong" orientation w.r.t. the protagonist we defend. By analyzing these different strategies, a contribution of this work is to provide a number of relevant parameters to take into account in developing and evaluating systems aiming at understanding natural language (NL) argumentations. The source of inspiration for this work is a corpus of 160 texts where each text describes a (different) car accident. Its result, for a given accident, is a set of first-order literals representing the essential facts of a description intended to defend one of the protagonists. An implementation in Answer Set Programming is underway. A couple of examples showing how to extract, from the same starting point, a defense for the two opposite sides are provided. Experimental validation of this work is in progress, and its first results are reported.

scholarly journals Proving Semantic Properties as First-Order Satisfiability (Extended Abstract)

2020 ◽  
Author(s):  
Salvador Lucas
Keyword(s):  
Logic Programming ◽  
Programming Languages ◽  
Answer Set Programming ◽  
Deductive Databases ◽  
Query Answering ◽  
Logical Theory ◽  
Data Bases ◽  
First Order ◽  
Computational Systems ◽  
Semantic Properties

The semantics of computational systems (e.g., relational and knowledge data bases, query-answering systems, programming languages, etc.) can often be expressed as (the specification of) a logical theory Th. Queries, goals, and claims about the behavior or features of the system can be expressed as formulas φ which should be checked with respect to the intended model of Th, which is often huge or even incomputable. In this paper we show how to prove such semantic properties φ of Th by just finding a model A of Th∪{φ}∪Zφ, where Zφ is an appropriate (possibly empty) theory depending on φ only. Applications to relational and deductive databases, rewriting-based systems, logic programming, and answer set programming are discussed.

scholarly journals Relational theories with null values and non-herbrand stable models

2012 ◽  
Vol 12 (4-5) ◽  
pp. 565-582 ◽  
Author(s):  
VLADIMIR LIFSCHITZ ◽  
KARL PICHOTTA ◽  
FANGKAI YANG
Keyword(s):  
Incomplete Information ◽  
Relational Databases ◽  
Logic Program ◽  
Answer Set Programming ◽  
First Order ◽  
Relational Theories ◽  
Null Values ◽  
Closure Assumption ◽  
General Method ◽  
Stable Models

AbstractGeneralized relational theories with null values in the sense of Reiter are first-order theories that provide a semantics for relational databases with incomplete information. In this paper we show that any such theory can be turned into an equivalent logic program, so that models of the theory can be generated using computational methods of answer set programming. As a step towards this goal, we develop a general method for calculating stable models under the domain closure assumption but without the unique name assumption.

scholarly journals Updates in answer set programming: An approach based on basic structural properties

2007 ◽  
Vol 7 (4) ◽  
pp. 451-479 ◽  
Author(s):  
MAURICIO OSORIO ◽  
VÍCTOR CUEVAS
Keyword(s):  
Structural Properties ◽  
Answer Set Programming ◽  
Interesting Property ◽  
Nonmonotonic Logic ◽  
Alternative Definition ◽  
Basic Properties ◽  
Definition Of ◽  
Weak Independence ◽  
Answer Sets ◽  
Answer Set

AbstractWe have studied the update operator ⊕1 defined for update sequences by Eiter et al. without tautologies and we have observed that it satisfies an interesting property. This property, which we call Weak Independence of Syntax (WIS), is similar to one of the postulates proposed by Alchourrón, Gärdenfors, and Makinson (AGM); only that in this case it applies to nonmonotonic logic. In addition, we consider other five additional basic properties about update programs and we show that ⊕1 satisfies them. This work continues the analysis of the AGM postulates with respect to the ⊕1 operator under a refined view that considers N2 as a monotonic logic which allows us to expand our understanding of answer sets. Moreover, N2 helped us to derive an alternative definition of ⊕1 avoiding the use of unnecessary extra atoms.

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