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12
The ProofTheory and Semantics of Intuitionistic Modal Logic
, 1994
"... Possible world semantics underlies many of the applications of modal logic in computer science and philosophy. The standard theory arises from interpreting the semantic definitions in the ordinary metatheory of informal classical mathematics. If, however, the same semantic definitions are interpret ..."
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Possible world semantics underlies many of the applications of modal logic in computer science and philosophy. The standard theory arises from interpreting the semantic definitions in the ordinary metatheory of informal classical mathematics. If, however, the same semantic definitions are interpreted in an intuitionistic metatheory then the induced modal logics no longer satisfy certain intuitionistically invalid principles. This thesis investigates the intuitionistic modal logics that arise in this way. Natural deduction systems for various intuitionistic modal logics are presented. From one point of view, these systems are selfjustifying in that a possible world interpretation of the modalities can be read off directly from the inference rules. A technical justification is given by the faithfulness of translations into intuitionistic firstorder logic. It is also established that, in many cases, the natural deduction systems induce wellknown intuitionistic modal logics, previously given by Hilbertstyle axiomatizations. The main benefit of the natural deduction systems over axiomatizations is their
Topical Categories of Domains
, 1997
"... this paper are algebraic dcpos, and many of the points discussed here will be needed later in the special case. 2 They provide a simple example to illustrate the "Display categories" in Section 3.2 ..."
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this paper are algebraic dcpos, and many of the points discussed here will be needed later in the special case. 2 They provide a simple example to illustrate the "Display categories" in Section 3.2
Geometric Logic As A Specification Language
 in: Hankin, Mackie and Nagarajan (eds), Theory and Formal Methods of Computing
"... The "observational content" of geometric logic is discussed and it is proposed that geometric logic is an appropriate basis for a Zlike specification language in which schemas are used as geometric theory presentations. ..."
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The "observational content" of geometric logic is discussed and it is proposed that geometric logic is an appropriate basis for a Zlike specification language in which schemas are used as geometric theory presentations.
Purity through Unravelling
 TECHNISCHE UNIVERSITÄT DRESDEN
, 2005
"... We divide attempts to give the structural proof theory of modal logics into two kinds, those pure formulations whose inference rules characterise modality completely by means of manipulations of boxes and diamonds, and those labelled formulations that leverage the use of labels in giving inferen ..."
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We divide attempts to give the structural proof theory of modal logics into two kinds, those pure formulations whose inference rules characterise modality completely by means of manipulations of boxes and diamonds, and those labelled formulations that leverage the use of labels in giving inference rules. The widespread adoption of labelled formulations is driven by their ability to model features of the model theory of modal logic in its proof theory. We describe
A Theorybased Topological Notion of Institution
 Recent Trends in Data Type Specification, volume 906 of Lecture
, 1995
"... . By adopting theories as primitive components of a logic and recognizing that formulae are just presentation details we arrive at the concept of topological institution. In a topological institution, we have, for each signature, a frame of theories, a set of interpretation structures and a satisfac ..."
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Cited by 3 (1 self)
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. By adopting theories as primitive components of a logic and recognizing that formulae are just presentation details we arrive at the concept of topological institution. In a topological institution, we have, for each signature, a frame of theories, a set of interpretation structures and a satisfaction relation. More precisely, we have, for each signature, a topological system. We show how to extract a topological institution from a given institution and establish an adjunction. Illustrations are given within the context of equational logic. We study the compositionality of theories. Formulae are recovered when we establish a general technique for presenting topological institutions. Topological institutions with finitely observable theories are shown to be useful in temporal monitoring applications where we would like to be able to characterize the properties of the system that can be monitored. Namely, an invariant property (G') cannot be monitored because it cannot be positively es...
Fundamentals of object oriented database modelling. Intellektual ~ny Sistemy (Intelligent Systems
 Intelligent Systems
, 1996
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A Topological View on Institutions
, 1994
"... By adopting theories as primitive components of a logic and recognizing that formulae are just presentation details we arrive at the concept of topological institution. In a topological institution, we have, for each signature, a frame of theories, a set of interpretation structures and a satisfa ..."
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Cited by 2 (1 self)
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By adopting theories as primitive components of a logic and recognizing that formulae are just presentation details we arrive at the concept of topological institution. In a topological institution, we have, for each signature, a frame of theories, a set of interpretation structures and a satisfaction relation. More precisely, we have, for each signature, a topological system. We show how to extract a topological institution from a given institution. Illustrations are given within the context of both equational and propositional logics. Already within the general setting of topological institutions we study the compositionality of theories and provide a characterization of both soundness and completeness. Formulae are recovered when we establish a general technique for presenting topological institutions. Equational and propositional topological institutions with finitely observable theories appear as simple applications of this technique. We consider and compare two notio...
On the border between functional programming and program synthesis
 Proceedings of the Estonian Academy of Sciences: Engineering
, 1998
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Tropological Systems and Observational Logic in Concurrency and Specification
"... Disserta,c~ao para obten,c~ao do Grau de Doutor em Matem'atica ..."
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