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The epistemic logic of IF games
, 2002
"... We analyze IF/hyperclassical games by bringing together two viewpoints from Jaakko Hintikka's work: game semantics, and epistemic logic. In the process, we link up between logic and game theory. ..."
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We analyze IF/hyperclassical games by bringing together two viewpoints from Jaakko Hintikka's work: game semantics, and epistemic logic. In the process, we link up between logic and game theory.
Correspondence and Completeness for Generalized Quantifiers.
 Bulletin of the IGPL
, 1994
"... this paper to explore this phenomenon, both its extent and its limits, in greater detail. As a first step, we introduce an analogue of the expansion of a language by Skolem functions. Consider a language L 82 which extends a firstorder language with equality by introducing a unary generalized quant ..."
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this paper to explore this phenomenon, both its extent and its limits, in greater detail. As a first step, we introduce an analogue of the expansion of a language by Skolem functions. Consider a language L 82 which extends a firstorder language with equality by introducing a unary generalized quantifier 2 x . We use this notation to emphasize an analogy between generalized quantifiers and modal operators, that will become apparent below. The dual of 2 x is 3 x ' = df :2 x :'. (In the examples above a filter quantifier would correspond to 2.)
The Categorial FineStructure of Natural Language
, 2003
"... Categorial grammar analyzes linguistic syntax and semantics in terms of type theory and lambda calculus. A major attraction of this approach is its unifying power, as its basic function/argument structures occur across the foundations of mathematics, language and computation. This paper considers, i ..."
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Categorial grammar analyzes linguistic syntax and semantics in terms of type theory and lambda calculus. A major attraction of this approach is its unifying power, as its basic function/argument structures occur across the foundations of mathematics, language and computation. This paper considers, in a light examplebased manner, where this elegant logical paradigm stands when confronted with the wear and tear of reality. Starting from a brief history of the Lambek tradition since the 1980s, we discuss three main issues: (a) the fit of the lambda calculus engine to characteristic semantic structures in natural language, (b) the coexistence of the original typetheoretic and more recent modal interpretations of categorial logics, and (c) the place of categorial grammars in the complex total architecture of natural language, which involves  amongst others  mixtures of interpretation and inference.
On One Decidable Generalized Quantifier Logic Corresponding to a Decidable Fragment of FirstOrder Logic
 Institute for Logic, Language and Computation, University of Amsterdam
, 1994
"... Van Lambalgen (1990) proposed a translation from a language containing a generalized quantifier Q into a firstorder language enriched with a family of predicates R i , for every arity i (or an infinitary predicate R) which takes QxOE(x; y 1 ; : : : ; yn ) to 8x(R(x; y 1 ; : : : ; yn ) ! OE(x; y 1 ..."
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Van Lambalgen (1990) proposed a translation from a language containing a generalized quantifier Q into a firstorder language enriched with a family of predicates R i , for every arity i (or an infinitary predicate R) which takes QxOE(x; y 1 ; : : : ; yn ) to 8x(R(x; y 1 ; : : : ; yn ) ! OE(x; y 1 ; : : : ; yn )) (y 1 ; : : : ; yn are precisely the free variables of QxOE). The logic of Q (without ordinary quantifiers) corresponds therefore to the fragment of firstorder logic which contains only specially restricted quantification. We prove that it is decidable using the method of semantic tableaux. Similar results were obtained by Andreka and Nemeti (1994) using the methods of algebraic logic. 1 Introduction Roughly speaking, in the history of modal logic modalities and their axioms came first and relational semantics giving them their precise meaning came second, bringing with it among other things the standard translation of modal logic into classical firstorder logic. Although...
Independence Structures In Set Theory
, 1996
"... This article, based on an invited lecture at the Logic Colloquium '93 in Keele, is a sequel to van Lambalgen [1992]. Apart from presenting new results, it differs from its predecessor in the following respects: (i) the presentation of the axioms is simplified, following some suggestions of Wojciec ..."
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This article, based on an invited lecture at the Logic Colloquium '93 in Keele, is a sequel to van Lambalgen [1992]. Apart from presenting new results, it differs from its predecessor in the following respects: (i) the presentation of the axioms is simplified, following some suggestions of Wojciech Buszkowski, (ii) the axioms have been strengthened, and (iii) the philosophical discussion has (hopefully) been improved. The article has appeared in W. Hodges et al (eds.), Logic: from Foundations to Applications (European Logic Colloquium), Oxford University Press 1996
In Conjunction With Qualitative Probability
 Annals of Pure and Applied Logic
, 1998
"... Numerical probabilities (associated with propositions) are eliminated in favor of qualitative notions, with an eye to isolating what it is about probabilities that is essential to judgments of acceptability. A basic choice point is whether the conjunction of two propositions, each (separately) ac ..."
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Numerical probabilities (associated with propositions) are eliminated in favor of qualitative notions, with an eye to isolating what it is about probabilities that is essential to judgments of acceptability. A basic choice point is whether the conjunction of two propositions, each (separately) acceptable, must be deemed acceptable. Concepts of acceptability closed under conjunction are analyzed within Keisler's weak logic for generalized quantifiers  or more specifically, filter quantifiers. In a different direction, the notion of a filter is generalized so as to allow sets with probability noninfinitesimally below 1 to be acceptable.
Natural Deduction for Sublogics of Predicate Logic
, 1997
"... This work gives a natural deduction presentations to some of the sublogic of predicate logic [vB94] and also to some of Alechina and J. van Benthem's sublogics. These presentations are based on [BM92, Ben95, Gab94] and Gabbay's Labelled Deductive System LDS [Gab94]. It also proves some correspondenc ..."
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This work gives a natural deduction presentations to some of the sublogic of predicate logic [vB94] and also to some of Alechina and J. van Benthem's sublogics. These presentations are based on [BM92, Ben95, Gab94] and Gabbay's Labelled Deductive System LDS [Gab94]. It also proves some correspondence results for the sublogics presented in [vB94] and some completeness theorem to the classes of models presented in [Ale95]. 1 Introduction In J. van Benthem [vB94], predicate logic is treated as a manymodal dynamic logic, and it is well known that some of these logics are decidable. The motivation is to investigate sublogics of first order logic that are decidable and still have usual desirable metaproperties (Craig interpolation, LosTarski Preservation and etc). According to Tarki's semantics, the notion of satisfaction of an existential formula 9xff in a given model M for an assignment s is defined as: M; s j= 9xff iff for some d 2 jM j, M; s d x j= ff. Whilst in Dynamic Semantics i...
Categorial Grammar at a CrossRoads
, 2003
"... Categorial grammars are driven by substructural logics. These are fragments of modal logics for the structures the grammar deals with. We will discuss modal language as a means of access to families of relevant structures: formal languages, type hierarchies, relation algebrasarrow models, and vect ..."
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Categorial grammars are driven by substructural logics. These are fragments of modal logics for the structures the grammar deals with. We will discuss modal language as a means of access to families of relevant structures: formal languages, type hierarchies, relation algebrasarrow models, and vector spaces. This is the crossroads of our title, where open directions abound.