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153
Probabilistic hyperspace analogue to language
 In Proceedings of the 28th Annual International ACM SIGIR conference on Research and development in information retrieval
, 2005
"... Song and Bruza [6] introduce a framework for Information Retrieval(IR) based on Gardenfor’s three tiered cognitive model; Conceptual Spaces[4]. They instantiate a conceptual space using Hyperspace Analogue to Language (HAL)[3] to generate higher order concepts which are later used for adhoc retrieva ..."
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Cited by 8 (5 self)
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Song and Bruza [6] introduce a framework for Information Retrieval(IR) based on Gardenfor’s three tiered cognitive model; Conceptual Spaces[4]. They instantiate a conceptual space using Hyperspace Analogue to Language (HAL)[3] to generate higher order concepts which are later used for adhoc retrieval. In this poster, we propose an alternative implementation of the conceptual space by using a probabilistic HAL space (pHAL). To evaluate whether converting to such an implementation is beneficial we have performed an initial investigation comparing the concept combination of HAL against pHAL for the task of query expansion. Our experiments indicate that pHAL outperforms the original HAL method and that better query term selection methods can improve performance on both HAL and pHAL.
Generalized Kripke Frames
, 2005
"... Algebraic work [9] shows that the deep theory of possible world semantics is available in the more general setting of substructural logics, at least in an algebraic guise. The question is whether it is also available in a relational form. This article seeks to set the stage for answering this questi ..."
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Cited by 8 (3 self)
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Algebraic work [9] shows that the deep theory of possible world semantics is available in the more general setting of substructural logics, at least in an algebraic guise. The question is whether it is also available in a relational form. This article seeks to set the stage for answering this question. Guided by the algebraic theory, but purely relationally we introduce a new type of frames. These structures generalize Kripke structures but are twosorted, containing both worlds and coworlds. These latter points may be viewed as modelling irreducible increases in information where worlds model irreducible decreases in information. Based on these structures, a purely model theoretic and uniform account of completeness for the implicationfusion fragment of various substructural logics is given. Completeness is obtained via a generalization of the standard canonical model construction in combination with correspondence results. 1
A KIF Formalization for the IFF Category Theory Ontology
, 2001
"... This paper begins the discussion of how the Information Flow Framework can be used to provide a principled foundation for the metalevel (or structural level) of the Standard Upper Ontology (SUO). This SUO structural level can be used as a logical framework for manipulating collections of ontologies ..."
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Cited by 7 (0 self)
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This paper begins the discussion of how the Information Flow Framework can be used to provide a principled foundation for the metalevel (or structural level) of the Standard Upper Ontology (SUO). This SUO structural level can be used as a logical framework for manipulating collections of ontologies in the object level of the SUO or other middle level or domain ontologies. From the Information Flow perspective, the SUO structural level resolves into several metalevel ontologies. This paper discusses a KIF formalization for one of those metalevel categories, the Category Theory Ontology. In particular, it discusses its category and colimit subnamespaces. The Information Flow Framework The mission of the Information Flow Framework (IFF) is to further the development of the theory of Information Flow, and to apply Information Flow to distributed logic, ontologies, and knowledge representation. IFF provides mechanisms for a principled foundation for an ontological framework  a framework for sharing ontologies, manipulating ontologies as objects, partitioning ontologies, composing ontologies, discussing ontological structure, noting dependencies between ontologies, declaring the use of other ontologies, etc. IFF is primarily based upon the theory of Information Flow initiated by Barwise (Barwise and Seligman 1997), which is centered on the notion of a classification. Information Flow itself based upon the theory of the Chu construction of autonomous categories (Barr 1996), thus giving it a connection to concurrency and Linear Logic. IFF is secondarily based upon the theory of Formal Concept Analysis initiated by Wille (Ganter & Wille 1999) , which is centered on the notion of a concept lattice. IFF represents metalogic, and as such operates at the structural level of ...
Information Integration in Institutions
, 2004
"... Abstract. This paper unifies and/or generalizes several approaches to information, including the information flow of Barwise and Seligman, the formal conceptual analysis of Wille, the lattice of theories of Sowa, the categorical general systems theory of Goguen, and the cognitive semantic theories o ..."
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Abstract. This paper unifies and/or generalizes several approaches to information, including the information flow of Barwise and Seligman, the formal conceptual analysis of Wille, the lattice of theories of Sowa, the categorical general systems theory of Goguen, and the cognitive semantic theories of Fauconnier, Turner, Gärdenfors, and others. Its rigorous approach uses category theory to achieve independence from any particular choice of representation, and institutions to achieve independence from any particular choice of logic. Corelations and colimits provide a general formalization of information integration, and Grothendieck constructions extend this to several kinds of heterogeneity. Applications include modular programming, CurryHoward isomorphism, database semantics, ontology alignment, cognitive semantics, and more. 1
A cartesian closed category of approximable concept structures
 Proceedings of the International Conference On Conceptual Structures
, 2004
"... Abstract. Infinite contexts and their corresponding lattices are of theoretical and practical interest since they may offer connections with and insights from other mathematical structures which are normally not restricted to the finite cases. In this paper we establish a systematic connection betwe ..."
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Abstract. Infinite contexts and their corresponding lattices are of theoretical and practical interest since they may offer connections with and insights from other mathematical structures which are normally not restricted to the finite cases. In this paper we establish a systematic connection between formal concept analysis and domain theory as a categorical equivalence, enriching the link between the two areas as outlined in [25]. Building on a new notion of approximable concept introduced by Zhang and Shen [26], this paper provides an appropriate notion of morphisms on formal contexts and shows that the resulting category is equivalent to (a) the category of complete algebraic lattices and Scott continuous functions, and (b) a category of information systems and approximable mappings. Since the latter categories are cartesian closed, we obtain a cartesian closed category of formal contexts that respects both the context structures as well as the intrinsic notion of approximable concepts at the same time. 1
Formalizing Botanical Taxonomies
 In Proceedings of the 11th International Conference on Conceptual Structures (ICCS’03), Springer LNAI 2746
, 2003
"... Because botanical taxonomies are prototypical classifications it would seem that it should be easy to formalize them as concept lattices or type hierarchies. ..."
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Because botanical taxonomies are prototypical classifications it would seem that it should be easy to formalize them as concept lattices or type hierarchies.
A quantum logic of down below
 Handbook of Quantum Logic, Quantum Structure, and Quantum Computation
"... The logic that was purposebuilt to accommodate the hopedfor reduction of arithmetic gave to language a dominant and pivotal place. Flowing from the founding efforts of Frege, Peirce, and Whitehead and Russell, this was a logic that incorporated proof theory into syntax, and in so doing made of gra ..."
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Cited by 5 (3 self)
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The logic that was purposebuilt to accommodate the hopedfor reduction of arithmetic gave to language a dominant and pivotal place. Flowing from the founding efforts of Frege, Peirce, and Whitehead and Russell, this was a logic that incorporated proof theory into syntax, and in so doing made of grammar
Metaphor and Information Flow
 IN: PROCEEDINGS OF THE 12TH MIDWEST ARTIFICIAL INTELLIGENCE AND COGNITIVE SCIENCE CONFERENCE
, 2001
"... This paper develops a formal model for metaphor and analogy built on information flow theory, formal concept analysis and conceptual graphs. Metaphor and analogy are important principles of human cognition based on representational maps. The model suggested in this paper defines metaphoric use ..."
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Cited by 5 (2 self)
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This paper develops a formal model for metaphor and analogy built on information flow theory, formal concept analysis and conceptual graphs. Metaphor and analogy are important principles of human cognition based on representational maps. The model suggested in this paper defines metaphoric use in terms of information transfer via an information channel with respect to contextual constraints.
Big toy models: Representing physical systems as Chu spaces. Synthese, 2011. Online First, April 2011. Available as arXiv:0910.2393
 m,n 33 S. Abramsky. Relational Hidden Variables and NonLocality. Studia Logica
, 2012
"... We pursue a modeloriented rather than axiomatic approach to the foundations of Quantum Mechanics, with the idea that new models can often suggest new axioms. This approach has often been fruitful in Logic and Theoretical Computer Science. Rather than seeking to construct a simplified toy model, we ..."
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We pursue a modeloriented rather than axiomatic approach to the foundations of Quantum Mechanics, with the idea that new models can often suggest new axioms. This approach has often been fruitful in Logic and Theoretical Computer Science. Rather than seeking to construct a simplified toy model, we aim for a ‘big toy model’, in which both quantum and classical systems can be faithfully represented — as well as, possibly, more exotic kinds of systems. To this end, we show how Chu spaces can be used to represent physical systems of various kinds. In particular, we show how quantum systems can be represented as Chu spaces over the unit interval in such a way that the Chu morphisms correspond exactly to the physically meaningful symmetries of the systems — the unitaries and antiunitaries. In this way we obtain a full and faithful functor from the groupoid of Hilbert spaces and their symmetries to Chu spaces. We also consider whether it is possible to use a finite value set rather than the unit interval; we show that three values suffice, while the two standard possibilistic reductions to two values both fail to preserve fullness. 1