462 research outputs found

    On the Limits of Second-Order Unification

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    Second-Order Unification is a problem that naturally arises when applying automated deduction techniques with variables denoting predicates. The problem is undecidable, but a considerable effort has been made in order to find decidable fragments, and understand the deep reasons of its complexity. Two variants of the problem, Bounded Second-Order Unification and Linear Second-Order Unification ¿where the use of bound variables in the instantiations is restricted¿, have been extensively studied in the last two decades. In this paper we summarize some decidability/undecidability/complexity results, trying to focus on those that could be more interesting for a wider audience, and involving less technical details.Peer Reviewe

    The undecidability of simultaneous rigid E-unification with two variables

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    Abstract. Recently it was proved that the problem of simultaneous rigid E-unification, or SREU, is undecidable. Here we show that 4 rigid equations with ground left-hand sides and 2 variables already imply undecidability. As a corollary we improve the undecidability result of the 3*-fragment of intuitionistic logic with equality. Our proof shows undecidability of a very restricted subset of the 33-fragment. Together with other results, it contributes to a complete characterization of decidability of the prenex fragment of intuitionistic logic with equality, in terms of the quantifier prefix. 1 I n t r o d u c t i o n Recently it was proved that the problem of simultaneous rigid E-unification (SREU) is undecidable Background of S R E U Simultaneous rigid E-unification was proposed by Ga~er, Raatz and Snyder 1 It has been noted by Gurevich and Veanes that 3 rigid equations suffice

    SAT Encoding of Unification in ELHR+ w.r.t. Cycle-Restricted Ontologies

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    Unification in Description Logics has been proposed as an inference service that can, for example, be used to detect redundancies in ontologies. For the Description Logic EL, which is used to define several large biomedical ontologies, unification is NP-complete. An NP unification algorithm for EL based on a translation into propositional satisfiability (SAT) has recently been presented. In this report, we extend this SAT encoding in two directions: on the one hand, we add general concept inclusion axioms, and on the other hand, we add role hierarchies (H) and transitive roles (R+). For the translation to be complete, however, the ontology needs to satisfy a certain cycle restriction. The SAT translation depends on a new rewriting-based characterization of subsumption w.r.t. ELHR+-ontologies

    Unification in the Description Logic EL w.r.t. Cycle-Restricted TBoxes

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    Unification in Description Logics (DLs) has been proposed as an inference service that can, for example, be used to detect redundancies in ontologies. The inexpressive Description Logic EL is of particular interest in this context since, on the one hand, several large biomedical ontologies are defined using EL. On the other hand, unification in EL has recently been shown to be NP-complete, and thus of significantly lower complexity than unification in other DLs of similarly restricted expressive power. However, the unification algorithms for EL developed so far cannot deal with general concept inclusion axioms (GCIs). This paper makes a considerable step towards addressing this problem, but the GCIs our new unification algorithm can deal with still need to satisfy a certain cycle restriction

    Unreduced Dynamic Complexity: Towards the Unified Science of Intelligent Communication Networks and Software

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    Operation of autonomic communication networks with complicated user-oriented functions should be described as unreduced many-body interaction process. The latter gives rise to complex-dynamic behaviour including fractally structured hierarchy of chaotically changing realisations. We recall the main results of the universal science of complexity (http://cogprints.org/4471/) based on the unreduced interaction problem solution and its application to various real systems, from nanobiosystems (http://cogprints.org/4527/) and quantum devices to intelligent networks (http://cogprints.org/4114/) and emerging consciousness (http://cogprints.org/3857/). We concentrate then on applications to autonomic communication leading to fundamentally substantiated, exact science of intelligent communication and software. It aims at unification of the whole diversity of complex information system behaviour, similar to the conventional, "Newtonian" science order for sequential, regular models of system dynamics. Basic principles and first applications of the unified science of complex-dynamic communication networks and software are outlined to demonstrate its advantages and emerging practical perspectives

    Constraint-based semantics

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    Montague\u27s famous characterization of the homomorphic relation between syntax and semantics naturally gives way in computational applications to CONSTRAINT-BASED formulations. This was originally motivated by the close harmony it provides with syntax, which is universally processed in a constraint-based fashion. Employing the same processing discipline in syntax and semantics allows that their processing (and indeed other processing) can be as tightly coupled as one wishes - indeed, there needn\u27t be any fundamental distinction between them at all. In this paper, we point out several advantages of the constraint-based view of semantics processing over standard views. These include (i) the opportunity to incorporate nonsyntactic constraints on semantics, such as those arising from phonology and context; (ii) the opportunity to formulate principles which generalize over syntax and semantics, such as those found in HEAD-DRIVEN PHRASE STRUCTURE GRAMMAR; (iii) a characterization of semantic ambiguity, which in turn provides a framework in which to describe disambiguation, and (iv) the opportunity to underspecify meanings in a way difficult to reconcile with other views. The last point is illustrated with an application to scope ambiguity in which a scheme is developed which underspecifies scope but eschews auxiliary levels of logical form
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