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A Coruña, Spain

Cabalar P.,University of Corunna | Santos P.E.,State University of Maringa
Artificial Intelligence | Year: 2016

This research note contains an extension of a previous work by Cabalar and Santos (2011) that formalised several spatial puzzles formed by strings and holes. That approach explicitly ignored some configurations and actions that were irrelevant for the studied puzzles but are physically possible and may become crucial for other spatial reasoning problems. In particular, the previous work did not consider the formation of string loops or the situations where a holed object is partially crossed by another holed object. In this paper, we remove these limitations by treating string loops as dynamic holes that can be created or destroyed by a pair of elementary actions, respectively picking or pulling from strings. We explain how string loops can be recognised in a data structure representing the domain states and define a notation to represent crossings through string loops. The resulting formalism is dual in the sense that it also allows understanding any hole as a kind of (sometimes rigid) closed string loop. © 2016 Published by Elsevier B.V. Source


Cabalar P.,University of Corunna
AI Communications | Year: 2011

In this paper we consider a logical treatment for the ordered disjunction operator × introduced by Brewka, Niemelä and Syrjänen in their Logic Programs with Ordered Disjunctions (LPOD). LPODs are used to represent preferences in logic programming under the answer set semantics. Their semantics is defined by first translating the LPOD into a set of normal programs (called split programs) and then imposing a preference relation among the answer sets of these split programs. We concentrate on the first step and show how a suitable translation of the ordered disjunction as a derived operator into the logic of Here-and-There allows capturing the answer sets of the split programs in a direct way. We use this characterisation not only for providing an alternative implementation for LPODs, but also for checking several properties (under strongly equivalent transformations) of the × operator, like for instance, its distributivity with respect to conjunction or regular disjunction. We also make a comparison to an extension proposed by Kärger, Lopes, Olmedilla and Polleres, that combines × with regular disjunction. © 2011 IOS Press and the authors. All rights reserved. Source


Dieguez M.,University of Corunna
Leibniz International Proceedings in Informatics, LIPIcs | Year: 2012

Answer Set Programming (ASP) has become a popular way for representing different kinds of scenarios from knowledge representation in Artificial Intelligence. Frequently, these scenarios involve a temporal component which must be considered. In ASP, time is usually represented as a variable whose values are defined by an extensional predicate with a finite domain. Dealing with a finite temporal interval has some disadvantages. First, checking the existence of a plan is not possible and second, it also makes difficult to decide whether two programs are strongly equivalent. If we extend the syntax of Answer Set Programming by using temporal operators from temporal modal logics, then infinite time can be considered, so the aforementioned disadvantages can be overcome. This extension constitutes, in fact, a formalism called Temporal Equilibrium Logic, which is based on Equilibrium Logic (a logical characterisation of ASP). Although recent contributions have shown promising results, Temporal Equilibrium Logic is still a novel paradigm and there are many gaps to fill. Our goal is to keep developing this paradigm, filling those gaps and turning it into a suitable framework for temporal reasoning. © Martín Diéguez. Source


Cabalar P.,University of Corunna
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2010

In previous work, the so-called Temporal Equilibrium Logic (TEL) was introduced. This formalism provides an extension of the Answer Set semantics for logic programs to arbitrary theories in the syntax of Linear Temporal Logic. It has already been shown that, in the non-temporal case, arbitrary propositional theories can always be reduced to logic program rules (with disjunction and negation in the head) independently on the context. That is, logic programs constitute a normal form for the non-temporal case. In this paper we show that TEL can be similarly reduced to a normal form consisting of a set of implications (embraced by a necessity operator) quite close to logic program rules. This normal form may be useful both for a practical implementation of TEL and a simpler analysis of theoretical problems. © 2010 Springer-Verlag. Source


Cabalar P.,University of Corunna
Theory and Practice of Logic Programming | Year: 2011

In this paper we propose an extension of Answer Set Programming (ASP) to deal with (possibly partial) evaluable functions. To this aim, we start from the most general logical counterpart of ASP, Quantified Equilibrium Logic (QEL), and propose a variant QEL= f where the set of functions is partitioned into Herbrand functions (or constructors) and evaluable functions (or operations). We show how this extension has a direct connection to Scott's Logic of Existence, and introduce several useful derived operators, some of them directly borrowed from Scott's formalisation. Using this general framework for arbitrary theories, we proceed to focus on a syntactic subclass that corresponds to normal logic programs with evaluable functions and equality. We provide a translation of this class into function-free normal programs and consider a safety condition so that the resulting program is also safe, under the usual meaning in ASP. Finally, we also establish a formal comparison to Lin and Wang's approach (FASP) dealing with evaluable total functions. © 2011 Cambridge University Press. Source

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