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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
Dialogue Pragmatics and Context Specification
 In Abduction, Belief and Context in Dialogue; studies in computational
, 2000
"... Introduction Pragmatics is commo,nly understood to be concerned with studying the relations between linguistic phenomena and properties of the context of use. The understanding of these relations is important in many areas of theoretical and applied research, from grammatical analysis to sociolingu ..."
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Cited by 58 (18 self)
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Introduction Pragmatics is commo,nly understood to be concerned with studying the relations between linguistic phenomena and properties of the context of use. The understanding of these relations is important in many areas of theoretical and applied research, from grammatical analysis to sociolinguistic field studies. One area where the importance of these relations has become particularly clear is the design of language understanding systems. Such systems are extremely limited, brittle, and unpractical if they do not have powerful ways to make use of contextual information in computing the meanings of utterances. The question of how this can be achieved in an effective and principled way forms one of the major obstacles in building such systems. Computational pragmatics, the study of how contextual information can be effectively brought to bear in language understanding and production processes, hopes to contribute to removing this obstacle. One way in which contextual infor
Canonical Propositional GentzenType Systems
 in Proceedings of the 1st International Joint Conference on Automated Reasoning (IJCAR 2001) (R. Goré, A Leitsch, T. Nipkow, Eds), LNAI 2083
, 2001
"... . Canonical propositional Gentzentype systems are systems which in addition to the standard axioms and structural rules have only pure logical rules which have the subformula property, introduce exactly one occurrence of a connective in their conclusion, and no other occurrence of any connectiv ..."
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. Canonical propositional Gentzentype systems are systems which in addition to the standard axioms and structural rules have only pure logical rules which have the subformula property, introduce exactly one occurrence of a connective in their conclusion, and no other occurrence of any connective is mentioned anywhere else in their formulation. We provide a constructive coherence criterion for the nontriviality of such systems, and show that a system of this kind admits cut elimination i it is coherent. We show also that the semantics of such systems is provided by nondeterministic twovalued matrices (2Nmatrices). 2Nmatrices form a natural generalization of the classical twovalued matrix, and every coherent canonical system is sound and complete for one of them. Conversely, with any 2Nmatrix it is possible to associate a coherent canonical Gentzentype system which has for each connective at most one introduction rule for each side, and is sound and complete for th...
The stories of logic and information
 In Handbook of the Philosophy of Information, P. Adriaans and
, 2008
"... ..."
Natural Deduction for NonClassical Logics
, 1996
"... We present a framework for machine implementation of families of nonclassical logics with Kripkestyle semantics. We decompose a logic into two interacting parts, each a natural deduction system: a base logic of labelled formulae, and a theory of labels characterizing the properties of the Kripke m ..."
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Cited by 13 (3 self)
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We present a framework for machine implementation of families of nonclassical logics with Kripkestyle semantics. We decompose a logic into two interacting parts, each a natural deduction system: a base logic of labelled formulae, and a theory of labels characterizing the properties of the Kripke models. By appropriate combinations we capture both partial and complete fragments of large families of nonclassical logics such as modal, relevance, and intuitionistic logics. Our approach is modular and supports uniform proofs of correctness and proof normalization. We have implemented our work in the Isabelle Logical Framework.
An Account of Natural Language Coordination in Type Theory with Coercive Subtyping
"... We discuss the semantics of NL coordination in modern type theories (MTTs) with coercive subtyping. The issue of conjoinable types is handled by means of a type universe of linguistic types. We discuss quantifier coordination, arguing that they should be allowed in principle and that the semantic i ..."
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We discuss the semantics of NL coordination in modern type theories (MTTs) with coercive subtyping. The issue of conjoinable types is handled by means of a type universe of linguistic types. We discuss quantifier coordination, arguing that they should be allowed in principle and that the semantic infelicity of some cases of quantifier coordination is due to the incompatible semantics of the relevant quantifiers. NonBoolean collective readings of conjunction are also discussed and, in particular, treated as involving the vectors of type Vec(A,n), an inductive family of types in an MTT. Lastly, the interaction between coordination and copredication is briefly discussed, showing that the proposed account of coordination and that of copredication by means of dottypes combine consistently as expected.
Conservative generalized quantifiers and presupposition
 XI. Cornell University
, 2001
"... Abstract. Conservativity in generalized quantifiers is linked to presupposition filtering, under a propositionsastypes analysis extended with dependent quantifiers. That analysis is underpinned by modeltheoretically interpretable proofs which inhabit propositions they prove, thereby providing obje ..."
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Abstract. Conservativity in generalized quantifiers is linked to presupposition filtering, under a propositionsastypes analysis extended with dependent quantifiers. That analysis is underpinned by modeltheoretically interpretable proofs which inhabit propositions they prove, thereby providing objects for quantification and hooks for anaphora. 1.
Adjectives in a Modern TypeTheoretical Setting
"... In this paper we discuss the semantics of adjectives from the perspective of a Modern Type Theory (MTT) with an adequate subtyping mechanism. In an MTT, common nouns (CNs) can be interpreted as types and, in particular, CNs modified by intersective and subsective adjectives can be given semantics by ..."
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In this paper we discuss the semantics of adjectives from the perspective of a Modern Type Theory (MTT) with an adequate subtyping mechanism. In an MTT, common nouns (CNs) can be interpreted as types and, in particular, CNs modified by intersective and subsective adjectives can be given semantics by means of Σtypes. However, an interpretation of CNs as types would not be viable without a proper notion of subtyping which, as we explain, is given by coercive subtyping, an adequate notion of subtyping for MTTs. It is also shown that suitable uses of universes are one of the key ingredients that have made such an analysis adequate. Privative and noncommittal adjectives require different treatments than the use of Σtypes. We propose to deal with privative adjectives using the disjoint union type while noncommittal adjectives by making use of the typetheoretical notion of context, as used by Ranta [27] to approximate the modeltheoretic notion of a possible world. Our approach to adjectives has a number of advantages over those proposed within the Montagovian setting, one of which is that the inferences related with the adjectives arise via typing and not by some kind of extra semantic meaning in the form of a meaning postulate.