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Wellfounded semantics for Boolean grammars
 INFORMATION AND COMPUTATION
, 2009
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An InfiniteGame Semantics for WellFounded Negation in Logic Programming
"... We present an infinitegame characterization of the wellfounded semantics for functionfree logic programs with negation. Our game is a simple generalization of the standard game for negationless logic programs introduced by M.H. van Emden (1986, Journal of Logic Programming, 3(1), 3753) in which ..."
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We present an infinitegame characterization of the wellfounded semantics for functionfree logic programs with negation. Our game is a simple generalization of the standard game for negationless logic programs introduced by M.H. van Emden (1986, Journal of Logic Programming, 3(1), 3753) in which two players, the Believer and the Doubter, compete by trying to prove (respectively disprove) a query. The standard game is equivalent to the minimum Herbrand model semantics of logic programming in the sense that a query succeeds in the minimum model semantics iff the Believer has a winning strategy for the game which begins with the Doubter doubting this query. The game for programs with negation that we propose follows the same rules as the standard one, except that the players swap roles every time the play “passes through ” negation. We start our investigation by establishing the determinacy of the new game by using some classical tools from the theory of infinitegames. Our determinacy result immediately provides a novel and purely gametheoretic characterization of the semantics of negation in logic programming. We proceed to establish the connections of the game semantics to the existing semantic approaches for logic programming with negation. For this purpose, we first define a refined version of the game that uses degrees of winning and losing for the two players. We then demonstrate that this refined game corresponds exactly to the infinitevalued minimum model semantics of negation (Rondogiannis & Wadge, 2005, ACM TOCL, 6(2), 441467). This immediately implies that the unrefined game is equivalent to the wellfounded semantics (since the infinitevalued semantics is a refinement of the wellfounded semantics).
A Extensional HigherOrder Logic Programming
"... We propose a purely extensional semantics for higherorder logic programming. In this semantics program predicates denote sets of ordered tuples, and two predicates are equal iff they are equal as sets. Moreover, every program has a unique minimum Herbrand model which is the greatest lower bound of ..."
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We propose a purely extensional semantics for higherorder logic programming. In this semantics program predicates denote sets of ordered tuples, and two predicates are equal iff they are equal as sets. Moreover, every program has a unique minimum Herbrand model which is the greatest lower bound of all Herbrand models of the program and the least fixedpoint of an immediate consequence operator. We also propose an SLDresolution proof system which is proven sound and complete with respect to the minimum Herbrand model semantics. In other words, we provide a purely extensional theoretical framework for higherorder logic programming which generalizes the familiar theory of classical (firstorder) logic programming.
A Purely ModelTheoretic Semantics for Disjunctive Logic Programs with Negation ⋆
"... Abstract. We present a purely modeltheoretic semantics for disjunctive logic programs with negation, building on the infinitevalued approach recently introduced for normal logic programs [9]. In particular, we show that every disjunctive logic program with negation has a nonempty set of minimal in ..."
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Abstract. We present a purely modeltheoretic semantics for disjunctive logic programs with negation, building on the infinitevalued approach recently introduced for normal logic programs [9]. In particular, we show that every disjunctive logic program with negation has a nonempty set of minimal infinitevalued models. Moreover, we show that the infinitevalued semantics can be equivalently defined using Kripke models, allowing us to prove some properties of the new semantics more concisely. In particular, for programs without negation, the new approach collapses to the usual minimal model semantics, and when restricted to normal logic programs, it collapses to the wellfounded semantics. Lastly, we show that every (propositional) program has a finite set of minimal infinitevalued models which can be identified by restricting attention to a finite subset of the truth values of the underlying logic. 1
Strong Equivalence of Logic Programs under the InfiniteValued Semantics
"... We consider the notion of strong equivalence [4] of normal propositional logic programs under the infinitevalued semantics [7] (which is a purely modeltheoretic semantics that is compatible with the wellfounded one). We demonstrate that two such programs are strongly equivalent under the infinite ..."
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We consider the notion of strong equivalence [4] of normal propositional logic programs under the infinitevalued semantics [7] (which is a purely modeltheoretic semantics that is compatible with the wellfounded one). We demonstrate that two such programs are strongly equivalent under the infinitevalued semantics if and only if they are logically equivalent in the infinitevalued logic of [7]. In particular, we show that strong equivalence of normal propositional logic programs is decidable, and more specifically coNPcomplete. Our results have a direct implication for the wellfounded semantics since, as we demonstrate, if two programs are strongly equivalent under the infinitevalued semantics, then they are also strongly equivalent under the wellfounded semantics. Keywords: Formal Semantics, Negation in Logic Programming, Strong Equivalence. 1
An Implementation of Prioritized Queries using the Google SOAP Search API
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Preferential Infinitesimals for Information Retrieval
"... Abstract. In this paper, we propose a preference framework for information retrieval in which the user and the system administrator are enabled to express preference annotations on search keywords and document elements, respectively. Our framework is flexible and allows expressing preferences such a ..."
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Abstract. In this paper, we propose a preference framework for information retrieval in which the user and the system administrator are enabled to express preference annotations on search keywords and document elements, respectively. Our framework is flexible and allows expressing preferences such as “A is infinitely more preferred than B, ” which we capture by using hyperreal numbers. Due to the widespread of XML as a standard for representing documents, we consider XML documents in this paper and propose a consistent preferential weighting scheme for nested document elements. We show how to naturally incorporate preferences on search keywords and document elements into an IR ranking process using the wellknown TFIDF ranking measure. 1
Preferential Regular Path Queries
"... Abstract. In this paper, we introduce preferential regular path queries. These are regular path queries whose symbols are annotated with preference weights for “scaling ” up or down the intrinsic importance of matching a symbol against a (semistructured) database edge label. Annotated regular path q ..."
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Abstract. In this paper, we introduce preferential regular path queries. These are regular path queries whose symbols are annotated with preference weights for “scaling ” up or down the intrinsic importance of matching a symbol against a (semistructured) database edge label. Annotated regular path queries are expressed syntactically as annotated regular expressions. We interpret these expressions in a uniform semiring framework, which allows different semantic interpretations for the same syntactic annotations. For our preference queries, we study three important aspects: (1) (progressive) query answering (2) (certain) query answering in LAV dataintegration systems, and (3) query containment and equivalence. In all of these, we obtain important positive results, which encourage the use of our preference framework for enhanced querying of semistructured databases. 1
Decision problems for partial specifications:
"... Partial specifications allow approximate models of systems such as Kripke structures, or labeled transition systems to be created. Using the abstraction possible with these models, an avoidance of the statespace explosion problem is possible, whilst still retaining a structure that can have propert ..."
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Partial specifications allow approximate models of systems such as Kripke structures, or labeled transition systems to be created. Using the abstraction possible with these models, an avoidance of the statespace explosion problem is possible, whilst still retaining a structure that can have properties checked over it. A single partial specification abstracts a set of systems, whether Kripke, labeled transition systems, or systems with both atomic propositions and named transitions. This thesis deals in part with problems arising from a desire to efficiently evaluate sentences of the modal µcalculus over a partial specification. Partial specifications also allow a single system to be modeled by a number of partial specifications, which abstract away different parts of the system. Alternatively, a number of partial specifications may represent different requirements on a system. The thesis also addresses the question of whether a set of partial specifications is consistent, that is to say, whether a single system exists that is abstracted by each member of the set. The effect of nominals, special atomic propositions true on only one state in a system, is also considered on the problem of the consistency of many partial specifications. The thesis also addresses the question of whether the systems a partial specification abstracts are all abstracted by a second partial specification, the problem of inclusion. The thesis demonstrates how commonly used “specification patterns ” – useful properties specified in the modal µcalculus, can be efficiently evaluated over partial specifications, and gives upper and lower complexity bounds on the problems related to sets of partial specifications. 3 4