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230
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
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.
A Formal Foundation for OntologyAlignment Interaction Models
"... Abstract. Ontology alignment foundations are hard to find in the literature. The abstract nature of the topic and the diverse means of practice make it difficult to capture it in a universal formal foundation. We argue that such a lack of formality hinders further development and convergence of prac ..."
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Cited by 8 (7 self)
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Abstract. Ontology alignment foundations are hard to find in the literature. The abstract nature of the topic and the diverse means of practice make it difficult to capture it in a universal formal foundation. We argue that such a lack of formality hinders further development and convergence of practices, and in particular, prevents us from achieving greater levels of automation. In this article we present a formal foundation for ontology alignment that is based on interaction models between heterogeneous agents on the Semantic Web. We use the mathematical notion of information flow in a distributed system to ground our three hypotheses of enabling semantic interoperability and we use a motivating example throughout the article: how to progressively align two ontologies of research quality assessment through meaning coordination. We conclude the article with the presentation—in an executable specification language—of such an ontologyalignment interaction model. 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 ...
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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Cited by 6 (4 self)
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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.
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
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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Cited by 5 (2 self)
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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
A formal model for situated semantic alignment
 Proceedings of the Sixth International Joint Conference on Autonomous Agents and Multiagent Systems. May 14–18, 2007. Honolulu, Hawai’i, 1270– 1277. International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS
, 2007
"... Ontology matching is currently a key technology to achieve the semantic alignment of ontological entities used by knowledgebased applications, and therefore to enable their interoperability in distributed environments such as multiagent systems. Most ontology matching mechanisms, however, assume ma ..."
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Cited by 5 (5 self)
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Ontology matching is currently a key technology to achieve the semantic alignment of ontological entities used by knowledgebased applications, and therefore to enable their interoperability in distributed environments such as multiagent systems. Most ontology matching mechanisms, however, assume matching prior integration and rely on semantics that has been coded a priori in concept hierarchies or external sources. In this paper, we present a formal model for a semantic alignment procedure that incrementally aligns differing conceptualisations of two or more agents relative to their respective perception of the environment or domain they are acting in. It hence makes the situation in which the alignment occurs explicit in the model. We resort to Channel Theory to carry out the formalisation.