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25
Cutfree Display Calculi for Relation Algebras
, 1997
"... . We extend Belnap's Display Logic to give a cutfree Gentzenstyle calculus for relation algebras. The calculus gives many axiomatic extensions of relation algebras by the addition of further structural rules. It also appears to be the first purely propositional Gentzenstyle calculus for rela ..."
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. We extend Belnap's Display Logic to give a cutfree Gentzenstyle calculus for relation algebras. The calculus gives many axiomatic extensions of relation algebras by the addition of further structural rules. It also appears to be the first purely propositional Gentzenstyle calculus for relation algebras. 1 Introduction Given a nonempty set U , the universal relation U \Theta U is the set of all ordered pairs (a; b) where a 2 U and b 2 U . Any subset of U \Theta U is a binary relation over U , and the set of all subsets of U \Theta U is the set of all binary relations over U . Thus any two binary relations R and S are each just a set of ordered pairs, and we can use the settheoretic operations of complement, intersection and union to build other relations. The identity relation is f(a; a) j a 2 Ug while the "relative" analogues of complement, intersection and union are converse (` R) = f(b; a) j (a; b) 2 Rg, composition (R ffi S) = f(a; b) j 9c; (a; c) 2 R and (c; b) 2 Sg and ...
A Logical Ontology
 Working with Conceptual Structures: Contributions to ICCS2000. Darmstadt (Germany
, 2000
"... . We make an attempt to develop a Peircean ontology that is presupposed by propositional logic. The result of this can be seen as a rst step towards linking Peirce's semiotic to his logic of relatives. Familiarity with Peirce's semiotic can be useful, but the thesis of this paper is in ..."
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Cited by 14 (14 self)
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. We make an attempt to develop a Peircean ontology that is presupposed by propositional logic. The result of this can be seen as a rst step towards linking Peirce's semiotic to his logic of relatives. Familiarity with Peirce's semiotic can be useful, but the thesis of this paper is intelligible without such a background. 1 Introduction The aim of this paper is to develop an ontology presupposed by propositional logic on the basis of Peirce's semiotic ([9]). It will be argued that his denitions of signs involve the meaning of a proposition in the formal logical sense. It will be shown that if, as Peirce maintains, logic is equivalent to semiotic, propositional logic can be derived from a Peircean semiotic. Peirce's classication of signs involves his triads, qualisignsinsignlegisign, iconindexsymbol, and rhemedicentargument. The importance of these triads has been emphasised by most Peirce scholars ([2], [7], [8], [10]). Although Peirce developed also larger systems of si...
ContentBased Text Querying With Ontological Descriptors
 Data and Knowledge Engineering
, 2004
"... This paper describes a method and a system for contentbased querying of texts based on the availability of an ontology for the concepts in the text domain. A key principle in the system is the extraction of conceptual content of noun phrases into descriptors forming an integral part of the ontology ..."
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Cited by 10 (4 self)
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This paper describes a method and a system for contentbased querying of texts based on the availability of an ontology for the concepts in the text domain. A key principle in the system is the extraction of conceptual content of noun phrases into descriptors forming an integral part of the ontology. The retrieval of text passages rests on matching descriptors from the text against descriptors from the noun phrases in the query. The match need not be exact but is mediated by the ontology, invoking in particular taxonomic reasoning with suband super concepts. The paper also reports on a prototype implementation of the system.
A Survey of Decidable FirstOrder Fragments and Description Logics
 Journal of Relational Methods in Computer Science
, 2004
"... The guarded fragment and its extensions and subfragments are often considered as a framework for investigating the properties of description logics. There are also other, some less wellknown, decidable fragments of firstorder logic which all have in common that they generalise the standard tran ..."
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The guarded fragment and its extensions and subfragments are often considered as a framework for investigating the properties of description logics. There are also other, some less wellknown, decidable fragments of firstorder logic which all have in common that they generalise the standard translation of to firstorder logic. We provide a short survey of some of these fragments and motivate why they are interesting with respect to description logics, mentioning also connections to other nonclassical logics.
Terminological Representation, Natural Language & Relation Algebra
, 1992
"... In this paper I establish a link between klonebased knowledge representation concerned with terminological representation and the work of P. Suppes (1976, 1979, 1981) and M. Bottner (1985, 1989) in computational linguistics. I show how this link can be utilised for the problem of finding adequate ..."
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Cited by 9 (2 self)
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In this paper I establish a link between klonebased knowledge representation concerned with terminological representation and the work of P. Suppes (1976, 1979, 1981) and M. Bottner (1985, 1989) in computational linguistics. I show how this link can be utilised for the problem of finding adequate terminological representations for given information formulated in ordinary English.
Two proof systems for Peirce algebras
 In Proc. RelMiCS7, vol. 3051 of LNCS
, 2004
"... Abstract. This paper develops and compares two tableauxstyle proof systems for Peirce algebras. One is a tableau refutation proof system, the other is a proof system in the style of RasiowaSikorski. 1 ..."
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Cited by 8 (4 self)
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Abstract. This paper develops and compares two tableauxstyle proof systems for Peirce algebras. One is a tableau refutation proof system, the other is a proof system in the style of RasiowaSikorski. 1
Firstorder resolution methods for modal logics
 In Volume in Memoriam of Harald Ganzinger, LNCS
, 2006
"... Abstract. In this paper we give an overview of results for modal logic which can be shown using techniques and methods from firstorder logic and resolution. Because of the breadth of the area and the many applications we focus on the use of firstorder resolution methods for modal logics. In additi ..."
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Cited by 6 (4 self)
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Abstract. In this paper we give an overview of results for modal logic which can be shown using techniques and methods from firstorder logic and resolution. Because of the breadth of the area and the many applications we focus on the use of firstorder resolution methods for modal logics. In addition to traditional propositional modal logics we consider more expressive PDLlike dynamic modal logics which are closely related to description logics. Without going into too much detail, we survey different ways of translating modal logics into firstorder logic, we explore different ways of using firstorder resolution theorem provers, and we discuss a variety of results which have been obtained in the setting of firstorder resolution. 1
Relational Grammars for Knowledge Representation
, 1996
"... This paper aims to enhance the practical applicability of relational grammars, which have been devised for the semantic analysis of natural language. We focus on their application in knowledge representation. In particular, we address how the representation problem for klonebased knowledge rep ..."
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Cited by 5 (1 self)
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This paper aims to enhance the practical applicability of relational grammars, which have been devised for the semantic analysis of natural language. We focus on their application in knowledge representation. In particular, we address how the representation problem for klonebased knowledge representation systems can be automatically solved with the help of relational grammars. New rules are presented for natural language formulations, like has sons and has at least two sons, commonly arising in application domains. For accommodating the latter kind of sentences we introduce a new class of socalled (concrete) graded Peirce algebras. A graded Peirce algebra is a Peirce algebra endowed with a countable set of numerical quantifier operations.
Equational axioms of test algebra
 Computer Science Logic, 11th International Workshop, CSL ’97, volume 1414 of LNCS
, 1997
"... We presentacomplete axiomatization of test algebra ([24, 18, 29]), the twosorted algebraic variant of Propositional Dynamic Logic (PDL, [21, 7]). The axiomatization consists of adding a nite number of equations to any axiomatization of Kleene algebra ([15, 26, 17, 4]) and algebraic translations of ..."
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Cited by 4 (0 self)
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We presentacomplete axiomatization of test algebra ([24, 18, 29]), the twosorted algebraic variant of Propositional Dynamic Logic (PDL, [21, 7]). The axiomatization consists of adding a nite number of equations to any axiomatization of Kleene algebra ([15, 26, 17, 4]) and algebraic translations of the Segerberg ([27]) axioms for PDL. Kleene algebras are not nitely axiomatizable ([25, 6]), so our result does not give us a nite axiomatization of test algebra: in fact, no nite equational axiomatization exists. We alsopresent a singlesorted version of test algebra, using the notion of dynamic negation ([9, 2, 11]), to which the previous results carry over. 1