Results 1  10
of
13
On Unification Problems in Restricted SecondOrder Languages
 In Annual Conf. of the European Ass. of Computer Science Logic (CSL98
, 1998
"... We review known results and improve known boundaries between the decidable and the undecidable cases of secondorder unification with various restrictions on secondorder variables. As a key tool we prove an undecidability result that provides a partial solution to an open problem about simultaneous ..."
Abstract

Cited by 7 (4 self)
 Add to MetaCart
We review known results and improve known boundaries between the decidable and the undecidable cases of secondorder unification with various restrictions on secondorder variables. As a key tool we prove an undecidability result that provides a partial solution to an open problem about simultaneous rigid Eunification.
Simultaneous rigid EUnification and other decision problems related to the Herbrand theorem
, 1998
"... Recently, a number of results have been published related to simultaneous rigid Eunification and Herbrand's theorem for logic with equality. The aim of this article is to overview these results, fill in some proofs that have only been sketched before, and present some new results. ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
Recently, a number of results have been published related to simultaneous rigid Eunification and Herbrand's theorem for logic with equality. The aim of this article is to overview these results, fill in some proofs that have only been sketched before, and present some new results.
Comparing Computational Representations of Herbrand Models
 Computational Logic and Proof Theory, 5th Kurt Godel Colloquium, KGC'97, volume 1289 of LNCS
, 1997
"... . Finding computationally valuable representations of models of predicate logic formulas is an important issue in the field of automated theorem proving, e.g. for automated model building or semantic resolution. In this article we treat the problem of representing single models independently of buil ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
. Finding computationally valuable representations of models of predicate logic formulas is an important issue in the field of automated theorem proving, e.g. for automated model building or semantic resolution. In this article we treat the problem of representing single models independently of building them and discuss the power of different mechanisms for this purpose. We start with investigating contextfree languages for representing single Herbrand models. We show their computational feasibility and prove their expressive power to be exactly the finite models. We show an equivalence with "ground atoms and ground equations" concluding equal expressive power. Finally we indicate how various other well known techniques could be used for representing essentially infinite models (i.e. models of not finitely controllable formulas), thus motivating our interest in relating model properties with syntactical properties of corresponding Herbrand models and in investigating connections betwe...
Using Grammars for Finite Domain Evaluation
 INT. WORKSHOP ON FIRSTORDER THEOREM PROVING (FTP'97), RISCLINZ REPORT SERIES NO. 9750
, 1997
"... In [8] we investigated representing Herbrand models via contextfree grammars and found the representation power of this method to be exactly the finite models. Based on these observations we now present a clause set evaluation algorithm that operates directly on grammars, avoiding the exponential ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
In [8] we investigated representing Herbrand models via contextfree grammars and found the representation power of this method to be exactly the finite models. Based on these observations we now present a clause set evaluation algorithm that operates directly on grammars, avoiding the exponential blowup from the number of nonterminals in the grammar to the number of elements in the finite domain of the corresponding model, ending up with a notsoobvious evaluation procedure for arbitrary clause sets over finite interpretations (specified via grammars).
SAT Encoding of Unification in ELHR+ w.r.t.
"... 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 NPcomplete. An NP unification algorithm for EL ..."
Abstract
 Add to MetaCart
(Show Context)
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 NPcomplete. 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 rewritingbased characterization of subsumption w.r.t. ELHR+ontologies. 1
Visiting Address:
"... Nonstandard inferences are particularly useful in the bottomup construction of ontologies in description logics. One of the more common nonstandard reasoning tasks is the most specific concept (msc) for an ABoxindividual. In this paper we present similar nonstandard reasoning task: most specif ..."
Abstract
 Add to MetaCart
(Show Context)
Nonstandard inferences are particularly useful in the bottomup construction of ontologies in description logics. One of the more common nonstandard reasoning tasks is the most specific concept (msc) for an ABoxindividual. In this paper we present similar nonstandard reasoning task: most specific concepts for models (modelmscs). We show that, although they look similar to ABoxmscs their computational behaviour can be different. We present constructions for modelmscs in FL0 and FLE with cyclic TBoxes and for ALC∪ ∗ with acyclic TBoxes. Since subsumption in FLE with cyclic TBoxes has not been examined previously, we present a characterization of subsumption and give a construction for the least common subsumer in this setting. 1
Strategies in RigidVariable Methods
"... We study complexity of methods using rigid variables, like the method of matings or the tableau method, on a decidable class of predicate calculus with equality. We show some intrinsic complications introduced by rigid variables. We also consider strategies for increasing multiplicity in rigidvaria ..."
Abstract
 Add to MetaCart
We study complexity of methods using rigid variables, like the method of matings or the tableau method, on a decidable class of predicate calculus with equality. We show some intrinsic complications introduced by rigid variables. We also consider strategies for increasing multiplicity in rigidvariable methods, and formally show that the use of intelligent strategies can result in an essential gain in efficiency. 1