146 research outputs found
A complete transformation system for polymorphic higher-order unification
Polymorphic higher-order unification is a method for unifying terms in the poly\-mor\-phi\-cally typed -calculus, that is, given a set of pairs of terms , called a unification problem, finding a substitution such that and are equivalent under the conversion rules of the calculus for all , . I present the method as a transformation system, i.e.\ as a set of schematic rules such that any unification problem can be transformed into where is an instantiation of the meta-level variables in and . By successive use of transformation rules one possibly obtains a solved unification problem with obvious unifier. I show that the transformation system is correct and complete, i.e.\if is an instance of a transformation rule, then the set of all unifiers of is a subset of the set of all unifiers of and if is the set of all unification problems that can be obtained from successive applications of transformation rules from an unification problem , then the union of the set of all unifiers of all unification problems in is the set of all unifiers of . The transformation rules presented here are essentially different from those in Gallier and Snyder (1989) or Nipkow (1990). The correctness and completeness proofs are in lines with those of Gallier and Snyder (1989)
Motel user manual
MOTEL is a logic-based knowledge representation languages of the KL-ONE family. It contains as a kernel the KRIS language which is a decidable sublanguage of first-order predicate logic. Whereas KRIS is a single-agent knowledge representation system, i.e. KRIS is only able to represent general world knowledge or the knowledge of one agent about the world, MOTEL is a multi-agent knowledge representation system. The MOTEL language allows modal contexts and modal concept forming operators which allow to represent and reason about the believes and wishes of multiple agents. Furthermore it is possible to represent defaults and stereotypes. Beside the basic resoning facilities for consistency checking, classification, and realization, MOTEL provides an abductive inference mechanism. Furthermore it is able to give explanations for its inferences
Modal Resolution: Proofs, Layers and Refinements
Resolution-based provers for multimodal normal logics require pruning of the search space for a proof in order to ameliorate the inherent intractability of the satisfiability problem for such logics. We present a clausal modal-layered hyper-resolution calculus for the basic multimodal logic, which divides the clause set according to the modal level at which clauses occur in order to reduce the number of possible inferences. We show that the calculus is complete for the logics being considered. We also show that the calculus can be combined with other strategies. In particular, we discuss the completeness of combining modal layering with negative and ordered resolution and provide experimental results comparing the different refinements
Comparative concept similarity over Minspaces: Axiomatisation and Tableaux Calculus
We study the logic of comparative concept similarity \CSL introduced by
Sheremet, Tishkovsky, Wolter and Zakharyaschev to capture a form of qualitative
similarity comparison. In this logic we can formulate assertions of the form "
objects A are more similar to B than to C". The semantics of this logic is
defined by structures equipped by distance functions evaluating the similarity
degree of objects. We consider here the particular case of the semantics
induced by \emph{minspaces}, the latter being distance spaces where the minimum
of a set of distances always exists. It turns out that the semantics over
arbitrary minspaces can be equivalently specified in terms of preferential
structures, typical of conditional logics. We first give a direct
axiomatisation of this logic over Minspaces. We next define a decision
procedure in the form of a tableaux calculus. Both the calculus and the
axiomatisation take advantage of the reformulation of the semantics in terms of
preferential structures.Comment: 25 page
Ontology-based data access with databases: a short course
Ontology-based data access (OBDA) is regarded as a key ingredient of the new generation of information systems. In the OBDA paradigm, an ontology defines a high-level global schema of (already existing) data sources and provides a vocabulary for user queries. An OBDA system rewrites such queries and ontologies into the vocabulary of the data sources and then delegates the actual query evaluation to a suitable query answering system such as a relational database management system or a datalog engine. In this chapter, we mainly focus on OBDA with the ontology language OWL 2QL, one of the three profiles of the W3C standard Web Ontology Language OWL 2, and relational databases, although other possible languages will also be discussed. We consider different types of conjunctive query rewriting and their succinctness, different architectures of OBDA systems, and give an overview of the OBDA system Ontop
A Foundational View on Integration Problems
The integration of reasoning and computation services across system and
language boundaries is a challenging problem of computer science. In this
paper, we use integration for the scenario where we have two systems that we
integrate by moving problems and solutions between them. While this scenario is
often approached from an engineering perspective, we take a foundational view.
Based on the generic declarative language MMT, we develop a theoretical
framework for system integration using theories and partial theory morphisms.
Because MMT permits representations of the meta-logical foundations themselves,
this includes integration across logics. We discuss safe and unsafe integration
schemes and devise a general form of safe integration
SAT-based Explicit LTL Reasoning
We present here a new explicit reasoning framework for linear temporal logic
(LTL), which is built on top of propositional satisfiability (SAT) solving. As
a proof-of-concept of this framework, we describe a new LTL satisfiability
tool, Aalta\_v2.0, which is built on top of the MiniSAT SAT solver. We test the
effectiveness of this approach by demonnstrating that Aalta\_v2.0 significantly
outperforms all existing LTL satisfiability solvers. Furthermore, we show that
the framework can be extended from propositional LTL to assertional LTL (where
we allow theory atoms), by replacing MiniSAT with the Z3 SMT solver, and
demonstrating that this can yield an exponential improvement in performance
Modal satisfiability via SMT solving
Modal logics extend classical propositional logic, and they are robustly decidable. Whereas most existing decision procedures for modal logics are based on tableau constructions, we propose a framework for obtaining decision procedures by adding instantiation rules to standard SAT and SMT solvers. Soundness, completeness, and termination of the procedures can be proved in a uniform and elementary way for the basic modal logic and some extensions.Fil: Areces, Carlos Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, AstronomÃa y FÃsica; Argentina.Fil: Areces, Carlos Eduardo. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentina.Fil: Fontaine, Pascal. Université de Lorraine; Francia.Fil: Fontaine, Pascal. National Institute for Research in Digital Science and Technology; Francia.Fil: Merz, Stephan. Université de Lorraine; Francia.Fil: Merz, Stephan. National Institute for Research in Digital Science and Technology; Francia.Ciencias de la Computació
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