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Analogical Mapping by Constraint Satisfaction
 COGNITIVE SCIENCE 13, 295 (1989)
, 1989
"... A theory of analogical mopping between source and target analogs based upon interacting structural, semantic, and pragmatic constraints is proposed here. The structural constraint of fsomorphfsm encourages mappings that maximize the consistency of relational corresondences between the elements of th ..."
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Cited by 283 (19 self)
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A theory of analogical mopping between source and target analogs based upon interacting structural, semantic, and pragmatic constraints is proposed here. The structural constraint of fsomorphfsm encourages mappings that maximize the consistency of relational corresondences between the elements of the two analogs. The constraint of semantic similarity supports mapping hypotheses to the degree that mapped predicates have similar meanings. The constraint of pragmatic centrality fovors mappings involving elements the analogist believes to be important in order to achieve the purpose for which the anology Is being used. The theory is implemented in a computer progrom called ACME (Analogical Constraint Mapping Engine), which represents constraints by means of a network of supporting and competing hypotheses regarding what elements to map. A coop erative algorithm for parallel constraint satisfaction identifies mapping hypotheses that collectively represent the overall mapping that best fits the interactlng constraints. ACME has been applied to a wide range of examples that include problem analogies, analogical arguments, explanatory analogies, story analogies, formal analogies, and metaphors. ACME is sensitive to semantic and prag matic information if it is available,.and yet able to compute mappings between formally isomorphic analogs without any similar or identical elements. The theory Is able to account for empirical findings regarding the impact of consistenty and similarity on human processing of analogies.
Dynamic Algebras as a wellbehaved fragment of Relation Algebras
 In Algebraic Logic and Universal Algebra in Computer Science, LNCS 425
, 1990
"... The varieties RA of relation algebras and DA of dynamic algebras are similar with regard to definitional capacity, admitting essentially the same equational definitions of converse and star. They differ with regard to completeness and decidability. The RA definitions that are incomplete with respect ..."
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Cited by 33 (5 self)
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The varieties RA of relation algebras and DA of dynamic algebras are similar with regard to definitional capacity, admitting essentially the same equational definitions of converse and star. They differ with regard to completeness and decidability. The RA definitions that are incomplete with respect to representable relation algebras, when expressed in their DA form are complete with respect to representable dynamic algebras. Moreover, whereas the theory of RA is undecidable, that of DA is decidable in exponential time. These results follow from representability of the free intensional dynamic algebras. Dept. of Computer Science, Stanford, CA 94305. This paper is based on a talk given at the conference Algebra and Computer Science, Ames, Iowa, June 24, 1988. It will appear in the proceedings of that conference, to be published by SpringerVerlag in the Lecture Notes in Computer Science series. This work was supported by the National Science Foundation under grant number CCR8814921 ...
Relation Algebras of Intervals
 ARTIFICIAL INTELLIGENCE
, 1994
"... Given a representation of a relation algebra we construct relation algebras of pairs and of intervals. If the representation happens to be complete, homogeneous and fully universal then the pair and interval algebras can be constructed direct from the relation algebra. If, further, the original rel ..."
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Cited by 15 (3 self)
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Given a representation of a relation algebra we construct relation algebras of pairs and of intervals. If the representation happens to be complete, homogeneous and fully universal then the pair and interval algebras can be constructed direct from the relation algebra. If, further, the original relation algebra is !categorical we show that the interval algebra is too. The complexity of relation algebras is studied and it is shown that every pair algebra with infinite representations is intractable. Applications include constructing an interval algebra that combines metric and interval expressivity.
Preference modelling
 State of the Art in Multiple Criteria Decision Analysis
, 2005
"... This paper provides the reader with a presentation of preference modelling fundamental notions as well as some recent results in this field. Preference modelling is an inevitable step in a variety of fields: economy, sociology, psychology, mathematical programming, even medicine, archaeology, and ob ..."
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Cited by 13 (0 self)
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This paper provides the reader with a presentation of preference modelling fundamental notions as well as some recent results in this field. Preference modelling is an inevitable step in a variety of fields: economy, sociology, psychology, mathematical programming, even medicine, archaeology, and obviously decision analysis. Our notation and some basic definitions, such as those of binary relation, properties and ordered sets, are presented at the beginning of the paper. We start by discussing different reasons for constructing a model or preference. We then go through a number of issues that influence the construction of preference models. Different formalisations besides classical logic such as fuzzy sets and nonclassical logics become necessary. We then present different types of preference structures reflecting the behavior of a decisionmaker: classical, extended and valued ones. It is relevant to have a numerical representation of preferences: functional representations, value functions. The concepts of thresholds and minimal representation are also introduced in this section. In section 7, we briefly explore the concept of deontic logic (logic of preference) and other formalisms associated with &quot;compact representation of preferences &quot; introduced for special purposes. We end the paper with some concluding remarks.
Do We Need Metamodels AND Ontologies for Engineering Platforms
 In Proceedings of the 1st ICSE Int. Workshop on Global Integrated Model Management
, 2006
"... In this paper we show how the joint use of metamodeling and ontologies allows to describe domain knowledge for a complex domain. Ontologies are used as stabilized descriptions of the business domain while metamodels allow a fine description of the domain (to be constructed in the initial phases of m ..."
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Cited by 6 (1 self)
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In this paper we show how the joint use of metamodeling and ontologies allows to describe domain knowledge for a complex domain. Ontologies are used as stabilized descriptions of the business domain while metamodels allow a fine description of the domain (to be constructed in the initial phases of modeling). We propose to use an ontology for anticipated categorization, i.e., as a “natural ” complement of the formal system which is induced by the metamodel. 1
The Discovery Of My Completeness Proofs
 Bulletin of Symbolic Logic
, 1996
"... This paper deals with aspects of my doctoral dissertation 1 ..."
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Cited by 5 (0 self)
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This paper deals with aspects of my doctoral dissertation 1
An FCA interpretation of Relation Algebra
, 2006
"... This paper discusses an interpretation of relation algebra and fork algebra with respect to FCA contexts. In this case, "relation algebra" refers to the DeMorganPeirceSchroederTarski algebra and not to the "relational algebra" as described by Codd. The goal of this interpre ..."
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Cited by 4 (3 self)
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This paper discusses an interpretation of relation algebra and fork algebra with respect to FCA contexts. In this case, "relation algebra" refers to the DeMorganPeirceSchroederTarski algebra and not to the "relational algebra" as described by Codd. The goal of this interpretation is to provide an algebraic formalisation of objectrelational databases that is based on binary relations and thus closer to FCA and formal contexts than the traditional formalisation based on Codd. The formalisation provides insights into certain symmetries (among quantifiers) and the use of ternary relations and partwhole relations for building relational databases.
Islands of tractability for relational constraints: towards dichotomy results for the description logic EL
"... EL is a tractable description logic serving as the logical underpinning of largescale ontologies. We launch a
systematic investigation of the boundary between tractable and intractable reasoning in EL under relational
constraints. E.g., we show that there are (modulo equivalence) exactly 3 universa ..."
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Cited by 3 (2 self)
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EL is a tractable description logic serving as the logical underpinning of largescale ontologies. We launch a
systematic investigation of the boundary between tractable and intractable reasoning in EL under relational
constraints. E.g., we show that there are (modulo equivalence) exactly 3 universal constraints on a transitive
and re#29;exive relation under which reasoning is tractable: being a singleton set, an equivalence relation, or
the empty constraint. We prove a number of results of this type and discuss a spectrum of open problems
including generalisations to the algebraic semantics for EL (semilattices with monotone operators).