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39
An introduction to substructural logics
, 2000
"... Abstract: This is a history of relevant and substructural logics, written for the Handbook of the History and Philosophy of Logic, edited by Dov Gabbay and John Woods. 1 1 ..."
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Cited by 139 (16 self)
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Abstract: This is a history of relevant and substructural logics, written for the Handbook of the History and Philosophy of Logic, edited by Dov Gabbay and John Woods. 1 1
Epistemic actions as resources
 Journal of Logic and Computation
, 2007
"... We provide algebraic semantics together with a sound and complete sequent calculus for information update due to epistemic actions. This semantics is flexible enough to accommodate incomplete as well as wrong information e.g. deceit. We give a purely algebraic treatment of the muddy children puzzle, ..."
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Cited by 19 (13 self)
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We provide algebraic semantics together with a sound and complete sequent calculus for information update due to epistemic actions. This semantics is flexible enough to accommodate incomplete as well as wrong information e.g. deceit. We give a purely algebraic treatment of the muddy children puzzle, which moreover extends to situations where the children are allowed to lie and cheat. Epistemic actions, that is, information exchanges between agents A, B,... ∈ A, are modeled as elements of a quantale, hence conceiving them as resources. Indeed, quantales are to locales what monoidal closed categories are to Cartesian closed categories, respectively providing semantics for Intuitionistic Logic, and for noncommutative Intuitionistic Linear Logic, including Lambek calculus. The quantale (Q, � , •) acts on an underlying Qright module (M, � ) of epistemic propositions and facts. The epistemic content is encoded by appearance maps, one pair f M A: M → M and f Q A: Q → Q of (lax) morphisms for each agent A ∈ A. By adjunction, they give rise to epistemic modalities [12], capturing the agents ’ knowledge on propositions and actions. The module action is epistemic update and gives rise to dynamic modalities [20] — cf. weakest preconditions. This model subsumes the crucial fragment of Baltag, Moss and Solecki’s [6] dynamic epistemic logic, abstracting it in a constructive fashion while introducing resourcesensitive structure on the epistemic actions. Keywords: Multiagent communication, knowledge update, resourcesensitivity, quantale, Galois adjoints, dynamic epistemic logic, sequent calculus, Lambek calculus, Linear Logic.
On the Emergent Semantic Web and Overlooked Issues
 In Proc. of the 3rd Intl. Semantic Web Conf. 2004. Japan
, 2004
"... The emergent Semantic Web, despite being in its infancy, has already received a lot of attention from academia and industry. This resulted in an abundance of prototype systems and discussion most of which are centred around the underlying infrastructure. However, when we critically review the wor ..."
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Cited by 15 (8 self)
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The emergent Semantic Web, despite being in its infancy, has already received a lot of attention from academia and industry. This resulted in an abundance of prototype systems and discussion most of which are centred around the underlying infrastructure. However, when we critically review the work done to date we realise that there is little discussion with respect to the vision of the Semantic Web. In particular, there is an observed dearth of discussion on how to deliver knowledge sharing in an environment such as the Semantic Web in effective and efficient manners. There are a lot of overlooked issues, associated with agents and trust to hidden assumptions made with respect to knowledge representation and robust reasoning in a distributed environment. These issues could potentially hinder further development if not considered at the early stages of designing Semantic Web systems. In this perspectives' paper, we aim to help engineers and practitioners of the Semantic Web by raising awareness of these issues.
Dynamic Odds & Ends
 Ethics
, 1998
"... Modal logic becomes action logic by adding programs as in propositional dynamic logic or the µ calculus. Modal languages can be seen as decidable fragments of firstorder logic that admit a natural bisimulation, and hence enjoy a good model theory. Recently, much stronger 'guarded fragments' of f ..."
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Cited by 13 (2 self)
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Modal logic becomes action logic by adding programs as in propositional dynamic logic or the µ calculus. Modal languages can be seen as decidable fragments of firstorder logic that admit a natural bisimulation, and hence enjoy a good model theory. Recently, much stronger 'guarded fragments' of firstorder logic have been identified that enjoy the same pleasant features. The latter can serve as richer action languages as well. We will develop the logic of guarded fragments as a form of process theory. ln particular, moving from sequential to parallel process operations correlates with moving to firstorder fragments that are close to, or perhaps just over the decidableundecidable fence. 1 The modal dynamics of actions We will start by reviewing the basics. Standard polymodal logic is a decidable fragment of the firstorder logic of process graphs (labeled transition systems, Kripke models). It can be characterized semantically as consisting, up to logical equivalence, of those firs...
Aligning logical and psychological perspectives on Diagrammatic Reasoning
 Artificial Intelligence Review
, 1999
"... We advance a theoretical framework... ..."
Formal support for representing and automating semantic interoperability
 In The Semantic Web: Research and Applications. ESWS 2004. Proceedings, LNCS 3053
, 2004
"... Abstract. Semantic interoperability has become a key issue for realizing the Semantic Web in its full potential. However, there is a lot of controversy regarding the meaning and scope of the term and scarce formal approaches to the problem of semantic heterogeneity. In this paper, we discuss these a ..."
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Cited by 9 (3 self)
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Abstract. Semantic interoperability has become a key issue for realizing the Semantic Web in its full potential. However, there is a lot of controversy regarding the meaning and scope of the term and scarce formal approaches to the problem of semantic heterogeneity. In this paper, we discuss these approaches and propose a formalisation of semantic interoperability based on the BarwiseSeligman theory of information flow. We argue for a theoretical framework that favours the analysis and implementation of semantic interoperability scenarios. We present an example case of such a scenario where our framework has been applied as well as variations of it in the domain of ontology mapping. 1
Duality for LatticeOrdered Algebras and for Normal Algebraizable Logics
 Studia Logica
, 1997
"... Part I of this paper is developed in the tradition of Stonetype dualities, where we present a new topological representation for general lattices (influenced by and abstracting over both Goldblatt's [17] and Urquhart's [46]), identifying them as the lattices of stable compactopens of their dual St ..."
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Cited by 8 (4 self)
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Part I of this paper is developed in the tradition of Stonetype dualities, where we present a new topological representation for general lattices (influenced by and abstracting over both Goldblatt's [17] and Urquhart's [46]), identifying them as the lattices of stable compactopens of their dual Stone spaces (stability refering to a closure operator on subsets). The representation is functorial and is extended to a full duality. In part II, we consider latticeordered algebras (lattices with additional operators) , extending the J'onsson and Tarski representation results [30] for Boolean algebras with Operators. Our work can be seen as developing, and indeed completing, Dunn's project of gaggle theory [13, 14]. We consider general lattices (rather than Boolean algebras), with a broad class of operators, which we dubb normal, and which includes the J'onssonTarski additive operators. Representation of `algebras is extended to full duality. In part III we discuss applications in logic...
Inheritance Reasoning: Psychological Plausibility, Proof Theory and Semantics
, 1995
"... Default inheritance reasoning is a propositional approach to nonmonotonic reasoning designed to model reasoning with natural language generics. Inheritance reasoners model sets of natural language generics as directed acyclic graphs, and inference corresponds to the specification of paths through th ..."
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Cited by 4 (2 self)
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Default inheritance reasoning is a propositional approach to nonmonotonic reasoning designed to model reasoning with natural language generics. Inheritance reasoners model sets of natural language generics as directed acyclic graphs, and inference corresponds to the specification of paths through those networks. A proliferation of inheritance proof theories exist in the literature along with extensive debate about the most reasonable way to construct inferences, based on intuitions about interpretations of particular inheritance networks. There has not been an accepted semantics for inheritance which unifies the set of possible proof theories, which would help identify truly illmotivated proof theories. This thesis attempts to clarify the inheritance literature in the three ways indicated in the title: psychological plausibility, proof theory and semantics. The thesis intends to displace debate about the best inferences to draw about a network from logicians ' introspections to empiri...
Compositional Structuring in the BMethod: A Logical Viewpoint of the Static Context
 in Proceedings of the International Conference of B and Z Users ZB2000
, 2000
"... The BMethod provides a collection of structuring mechanisms which support information hiding, modularisation and compositionality of module operations, although, in order to achieve compositionality and independent (parallel) refinement, sharing is restricted in B. In this paper we elaborate some n ..."
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Cited by 4 (3 self)
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The BMethod provides a collection of structuring mechanisms which support information hiding, modularisation and compositionality of module operations, although, in order to achieve compositionality and independent (parallel) refinement, sharing is restricted in B. In this paper we elaborate some noninterference and compositionality assumptions that underlie structuring mechanisms such as uses, sees and imports and show how they may be violated by inducing emerging properties which alter the context of the used, seen or imported machine. We discuss how such situations can be avoided by considering necessary and sufficient conditions for logical conservativeness and modularisation. As proof obligations, these conditions ensure that the properties of the context of the seen, used or imported component are conserved, i.e. that they are preserved but not enriched. From a logical viewpoint, these proof obligations require that the uniform interpolant of the contextual extension axioms is implied by the base context.
A Minimal Calculus for Situated MultiAgent Systems
 in eProceedings, SSGRR03w (Advances in Infrastructures for eBusiness
, 2003
"... We present a processalgebraic approach to situated multiagent systems which incorporates syntax for agent systems as well as for the environments (workspaces) they live in. Agent states are characterized by (1) a belief state, (2) a goal (desire, need) state and (3) a capabilities state. Capabilit ..."
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Cited by 3 (3 self)
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We present a processalgebraic approach to situated multiagent systems which incorporates syntax for agent systems as well as for the environments (workspaces) they live in. Agent states are characterized by (1) a belief state, (2) a goal (desire, need) state and (3) a capabilities state. Capabilities are determined by a subspace of the workspace the agent lives in, and they are represented in the agent state as a collection of types of objects (tools, in the agent's workspace) the agent has the expertise (or permission) to use. Action capabilities are then just permissible transformations of workspaces, restricted to the particular capabilities space of the agent. Workspaces (certain kinds of collections of objects, modelled here as simply typed records of labelled attributes) and workspace transformations (record update operations) are structured into a transition system. We use a simple model of objects as records and, therefore, of workspaces and thus we only deal in this report with deterministic environments. Transitions are determined by agent actions (modifications of properties of objects in their capabilities space, modelled as record update operations), thus allowing for a formal account of agent systems living in an ever changing environment. Beliefs and desires are formulae of a manysorted, firstorder multimodal language of properties of workspaces, where sorts are object types and modalities are indexed by workspace transformations (record updates). The logical language is kept simple, allowing only for firstorder beliefs (beliefs about properties of workspaces). We present a language of situated, cooperative, selfinterested agent systems, proposing a basic collection of agent behaviors (including ground observation actions, commitments, communication via assertions and requests, recursive behaviors, choice, concurrent behaviors etc), we provide an operational semantics for this language and discuss some examples of useful definable agent behaviors, such as perceiving (performing observations triggered by a statement). We then present and discuss notions of (behavioral) agent preorder and equivalence relations. Using the operational semantics and our notion of behavioral preorder and equivalence we propose an inequational theory for reasoning about agents. We conclude with presenting and discussing a case study for a simple agent system.