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76
Some Foundational Questions Concerning Language
 Journal of Pragmatics
, 1992
"... foundations of standard approaches to language studies involve an incoherence in their presuppositions. Second, we present an alternative approach that resolves this incoherence. Third, we discuss how this error manifests itself in categorial grammars and model theoretic possible worlds semantics ..."
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Cited by 22 (21 self)
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foundations of standard approaches to language studies involve an incoherence in their presuppositions. Second, we present an alternative approach that resolves this incoherence. Third, we discuss how this error manifests itself in categorial grammars and model theoretic possible worlds semantics. Fourth, we suggest some possible revisions in standard approaches to accommodate them to the alternative that we suggest. We arrive at a fundamentally functional, or pragmatic, conception  an interactive conception  of the nature of language and meaning. Contents 1.
Computation in Valuation Algebras
 IN HANDBOOK OF DEFEASIBLE REASONING AND UNCERTAINTY MANAGEMENT SYSTEMS, VOLUME 5: ALGORITHMS FOR UNCERTAINTY AND DEFEASIBLE REASONING
, 1999
"... Many different formalisms for treating uncertainty or, more generally, information and knowledge, have a common underlying algebraic structure. ..."
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Cited by 22 (4 self)
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Many different formalisms for treating uncertainty or, more generally, information and knowledge, have a common underlying algebraic structure.
On The Algebraic Models Of Lambda Calculus
 Theoretical Computer Science
, 1997
"... . The variety (equational class) of lambda abstraction algebras was introduced to algebraize the untyped lambda calculus in the same way Boolean algebras algebraize the classical propositional calculus. The equational theory of lambda abstraction algebras is intended as an alternative to combinatory ..."
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Cited by 20 (11 self)
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. The variety (equational class) of lambda abstraction algebras was introduced to algebraize the untyped lambda calculus in the same way Boolean algebras algebraize the classical propositional calculus. The equational theory of lambda abstraction algebras is intended as an alternative to combinatory logic in this regard since it is a firstorder algebraic description of lambda calculus, which allows to keep the lambda notation and hence all the functional intuitions. In this paper we show that the lattice of the subvarieties of lambda abstraction algebras is isomorphic to the lattice of lambda theories of the lambda calculus; for every variety of lambda abstraction algebras there exists exactly one lambda theory whose term algebra generates the variety. For example, the variety generated by the term algebra of the minimal lambda theory is the variety of all lambda abstraction algebras. This result is applied to obtain a generalization of the genericity lemma of finitary lambda calculus...
A RelationAlgebraic Approach to the Region Connection Calculus
 Fundamenta Informaticae
, 2001
"... We explore the relationalgebraic aspects of the region connection calculus (RCC) of Randell et al. (1992a). In particular, we present a refinement of the RCC8 table which shows that the axioms provide for more relations than are listed in the present table. We also show that each RCC model leads ..."
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Cited by 19 (0 self)
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We explore the relationalgebraic aspects of the region connection calculus (RCC) of Randell et al. (1992a). In particular, we present a refinement of the RCC8 table which shows that the axioms provide for more relations than are listed in the present table. We also show that each RCC model leads to a Boolean algebra. Finally, we prove that a refined version of the RCC5 table has as models all atomless Boolean algebras B with the natural ordering as the "part  of" relation, and that the table is closed under first order definable relations iff B is homogeneous. 1 Introduction Qualitative reasoning (QR) has its origins in the exploration of properties of physical systems when numerical information is not sufficient  or not present  to explain the situation at hand (Weld and Kleer, 1990). Furthermore, it is a tool to represent the abstractions of researchers who are constructing numerical systems which model the physical world. Thus, it fills a gap in data modeling which often l...
Class Library Implementation of an Open Architecture Knowledge Support System
, 1994
"... Objectoriented class libraries offer the potential for individual researchers to manage the large bodies of code generated in the experimental development of complex interactive systems. This article analyzes the structure of such a class library that supports the rapid prototyping of a wide range ..."
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Cited by 19 (10 self)
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Objectoriented class libraries offer the potential for individual researchers to manage the large bodies of code generated in the experimental development of complex interactive systems. This article analyzes the structure of such a class library that supports the rapid prototyping of a wide range of systems including collaborative networking, shared documents, hypermedia, machine learning, knowledge acquisition and knowledge representation, and various combinations of these technologies. The overall systems architecture is presented in terms of a heterogeneous collection of systems providing a wide range of application functionalities. Examples are given of group writing, multimedia and knowledgebased systems which are based on combining these functionalities. The detailed design issues of the knowledge representation server component of the system are analyzed in terms of requirements, current stateoftheart, and the underlying theoretical principles that lead to an effective obj...
Higher Order Logic
 In Handbook of Logic in Artificial Intelligence and Logic Programming
, 1994
"... Contents 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2 The expressive power of second order Logic : : : : : : : : : : : 3 2.1 The language of second order logic : : : : : : : : : : : : : 3 2.2 Expressing size : : : : : : : : : : : : : : : : : : : : : : : : 4 2.3 Definin ..."
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Cited by 18 (0 self)
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Contents 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2 The expressive power of second order Logic : : : : : : : : : : : 3 2.1 The language of second order logic : : : : : : : : : : : : : 3 2.2 Expressing size : : : : : : : : : : : : : : : : : : : : : : : : 4 2.3 Defining data types : : : : : : : : : : : : : : : : : : : : : 6 2.4 Describing processes : : : : : : : : : : : : : : : : : : : : : 8 2.5 Expressing convergence using second order validity : : : : : : : : : : : : : : : : : : : : : : : : : 9 2.6 Truth definitions: the analytical hierarchy : : : : : : : : 10 2.7 Inductive definitions : : : : : : : : : : : : : : : : : : : : : 13 3 Canonical semantics of higher order logic : : : : : : : : : : : : 15 3.1 Tarskian semantics of second order logic : : : : : : : : : 15 3.2 Function and re
A Logic for Rough Sets
 Theoretical Computer Science
, 1997
"... The collection of all subsets of a set forms a Boolean algebra under the usual set theoretic operations, while the collection of rough sets of an approximation space is a regular double Stone algebra [24]. The appropriate class of algebras for classical propositional logic are Boolean algebras, and ..."
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Cited by 17 (4 self)
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The collection of all subsets of a set forms a Boolean algebra under the usual set theoretic operations, while the collection of rough sets of an approximation space is a regular double Stone algebra [24]. The appropriate class of algebras for classical propositional logic are Boolean algebras, and it is reasonable to assume that regular double Stone algebras are a class of algebras appropriate for a logic of rough sets. Using the representation theorem for these algebras by Katrink [16], we present such a logic for rough sets and its algebraic semantics in the spirit of Andrka et al [2]. keywords: Rough sets, algebraic semantics, regular double Stone algebras 1 Introduction Rough set data analysis has been developed by Pawlak and his coworkers since the early 1980s as a method of dealing with coarse information. We invite the reader to consult the monographs by Pawlak [23] and Sl/owinski [26] for an in depth exposition of the theory and its applications. The building blocks of rough...
COMPLEXITY OF EQUATIONS VALID IN ALGEBRAS OF RELATIONS  Part II: Finite axiomatizations.
"... We study algebras whose elements are relations, and the operations are natural "manipulations" of relations. This area goes back to 140 years ago to works of De Morgan, Peirce, Schroder (who expanded the Boolean tradition with extra operators to handle algebras of binary relations). Well known exam ..."
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Cited by 17 (2 self)
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We study algebras whose elements are relations, and the operations are natural "manipulations" of relations. This area goes back to 140 years ago to works of De Morgan, Peirce, Schroder (who expanded the Boolean tradition with extra operators to handle algebras of binary relations). Well known examples of algebras of relations are the varieties RCAn of cylindric algebras of nary relations, RPEAn of polyadic equality algebras of nary relations, and RRA of binary relations with composition. We prove that any axiomatization, say E, of RCAn has to be very complex in the following sense: for every natural number k there is an equation in E containing more than k distinct variables and all the operation symbols, if 2 ! n ! !. Completely analogous statement holds for the case n !. This improves Monk's famous nonfinitizability theorem for which we give here a simple proof. We prove analogous nonfinitizability properties of the larger varieties SNrnCA n+k . We prove that the complementa...
Hindley/Milner style type systems in constraint form
, 1999
"... This papers describes Hindley/Milner style type systems in constraint form. Previously, many type descriptions have still been partially represented in the type language. We argue that this can lead to shortcomings in the type and inference system. Examples are given to support this statement. As a ..."
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Cited by 16 (1 self)
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This papers describes Hindley/Milner style type systems in constraint form. Previously, many type descriptions have still been partially represented in the type language. We argue that this can lead to shortcomings in the type and inference system. Examples are given to support this statement. As a solution we present a purely constraintbased formulation of Hindley/Milner style type systems which enjoys much nicer logical properties than previous approaches. More specifically, we present a solution to the open problem of type inference in nonregular theories.
Representability is not decidable for finite relation algebras
 Trans. Amer. Math. Soc
, 1999
"... Abstract. We prove that there is no algorithm that decides whether a finite relation algebra is representable. Representability of a finite relation algebra A is determined by playing a certain two player game G(A) over ‘atomic Anetworks’. It can be shown that the second player in this game has a w ..."
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Cited by 15 (6 self)
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Abstract. We prove that there is no algorithm that decides whether a finite relation algebra is representable. Representability of a finite relation algebra A is determined by playing a certain two player game G(A) over ‘atomic Anetworks’. It can be shown that the second player in this game has a winning strategy if and only if A is representable. Let τ be a finite set of square tiles, where each edge of each tile has a colour. Suppose τ includes a special tile whose four edges are all the same colour, a colour not used by any other tile. The tiling problem we use is this: is it the case that for each tile T ∈ τ there is a tiling of the plane Z × Z using only tiles from τ in which edge colours of adjacent tiles match and with T placed at (0, 0)? It is not hard to show that this problem is undecidable. From an instance of this tiling problem τ, we construct a finite relation algebra RA(τ) and show that the second player has a winning strategy in G(RA(τ)) if and only if τ is a yesinstance. This reduces the tiling problem to the representation problem and proves the latter’s undecidability. 1.