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46
A Cutfree Sequent Calculus for Elementary Situated Reasoning
, 1991
"... A rstorder language is interpreted in the following way: terms are regarded as referring to situations and the truth of formulae is relativized to a situation. The language is then extended to include formulae of the form t : (where t is a term and is a formula) meaning that is true in the s ..."
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A rstorder language is interpreted in the following way: terms are regarded as referring to situations and the truth of formulae is relativized to a situation. The language is then extended to include formulae of the form t : (where t is a term and is a formula) meaning that is true in the situation referred to by t. Gentzen's sequent calculus for classical rstorder logic is extended with rules which capture this interpretation. Variants of the calculus and extensions of the language are discussed and the Cut rule is shown to be eliminable from some of the proposed calculi. Situation theory has been concerned with a range of issues centring around the partiality, context dependency and intensional structure of information. In formalizing situation theory one must focus on a specic aspect of the whole package  there is too much uncertainty and equivocation about the connections between the various parts. A dominant approach in recent years has been to focus on build...
Direct reference and implicature
 Philosophical Studies
, 1998
"... I. According to some formulations of the theory of Direct Reference the semantic value, relative to a context of utterance, of rigid singular terms such as proper names and indexicals is just their referent. This position seems to preclude an accurate account of such terms as they behave in natural ..."
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I. According to some formulations of the theory of Direct Reference the semantic value, relative to a context of utterance, of rigid singular terms such as proper names and indexicals is just their referent. This position seems to preclude an accurate account of such terms as they behave in natural languages, since it is easy to construct examples of coreferential rigid singular terms embedded into sentential contexts in which it appears that those terms must be contributing different semantic values to those sentences. Yet because, among other things, of the difficulties facing Fregean alternatives to Direct Reference some authors have attempted to defuse the apparent counterexamples to that theory by arguing that these examples evince pragmatic rather than semantic phenomena. According to this view the difference between two sentences that are alike except for containing distinct but coreferential rigid singular terms is that they convey different suggestions or insinuations; two such sentences nevertheless have identical semantic content and, in particular, identical truth conditions. 1 In attempting to substantiate this point some proponents of this line of defense of Direct Reference have suggested that the pragmatic difference between the sentences in
There are no abstract objects
 In
, 2008
"... Suppose you start out inclined towards the hardheaded view that the world of material objects is the whole of reality. You elaborate: ‘Everything there is is a material object: the sort of thing you could bump into; the sort of thing for which it would be sensible to ask how much it weighs, what sh ..."
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Suppose you start out inclined towards the hardheaded view that the world of material objects is the whole of reality. You elaborate: ‘Everything there is is a material object: the sort of thing you could bump into; the sort of thing for which it would be sensible to ask how much it weighs, what shape it is, how fast it is moving, and how far it is from other material objects. There is nothing else. ’ You develop some practice defending your thesis from the expected objections, from believers in ghosts, God, immaterial souls, Absolute Space, and so on. None of this practice will do you much good the first time you are confronted with the following objection: What about numbers and properties? These are obviously not material objects. It would be crazy to think that you might bump into the number two, or the property of having many legs. One would have to be confused to wonder how much these items weigh, or how far away they are. But obviously there are numbers and properties. Surely even you don’t deny that there are four prime numbers between one and ten, or that spiders and insects share many important anatomical properties. 1 But these wellknown truths evidently imply that there are numbers, and that there are properties. So
An expressive firstorder logic with flexible typing for natural language semantics
 Logic Journal of the Interest Group in Pure ans Applied Logics 12(2):135–168
, 2003
"... We present Property Theory with Curry Typing (PTCT), an intensional firstorder logic for natural language semantics. PTCT permits finegrained specifications of meaning. It also supports polymorphic types and separation types. 1 We develop an intensional number theory within PTCT in order to repres ..."
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We present Property Theory with Curry Typing (PTCT), an intensional firstorder logic for natural language semantics. PTCT permits finegrained specifications of meaning. It also supports polymorphic types and separation types. 1 We develop an intensional number theory within PTCT in order to represent proportional generalized quantifiers like most. We use the type system and our treatment of generalized quantifiers in natural language to construct a typetheoretic approach to pronominal anaphora that avoids some of the difficulties that undermine previous typetheoretic analyses of this phenomenon. 1
The Nature of Epistemic Space
 Causality, Interpretation, and the Mind. Oxford: Oxford UP. � Chudnoff, E. Forthcoming. “Intellectual Gestalts.” In T. Horgan and U. Kriegel (eds.), Phenomenal Intentionality: New Essays. Oxford and
, 1994
"... There are many ways things might be, for all I know. For all I know, it might be that there is life on Jupiter, and it might be that there is not. It might be that Australia will win the next Ashes series, and it might be that they will not. It might be that my greatgrandfather was my greatgrandmo ..."
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There are many ways things might be, for all I know. For all I know, it might be that there is life on Jupiter, and it might be that there is not. It might be that Australia will win the next Ashes series, and it might be that they will not. It might be that my greatgrandfather was my greatgrandmother’s second cousin, and it might be that he was not. It might be that brass is a compound, and it might be that it is not. There are even more ways things might be, for all I know with certainty. It might be that there are three chairs in this room, and it might be that there are not. It might be that water is H2O, and it might be that it is not. It might be that my father was born in Egypt, and it might be that he was not. It might be that I have a body, and it might be that I do not. We normally say that it is epistemically possible for a subject that p, when it might be that p for all the subject knows. So it is epistemically possible for me that there is life on Jupiter, or that brass is a compound. One can define various different standards of epistemic possibility, corresponding to various different standards for knowledge. For example, one might say that it is epistemically possible in the Cartesian sense (for a subject) that p when it might be that p, for all a subject knows with certainty. So in the Cartesian sense, it is epistemically possible for me that water is not H2O, and it is epistemically possible for me that I do not have a body. A natural way to think about epistemic possibility is as follows. When it is epistemically possible (for a subject) that p, there is an epistemically possible scenario (for that subject) in
Set Theory and Nominalisation, Part I
 Journal of Logic and Computation
, 1996
"... This paper argues that the basic problems of nominalisation are those of set theory. We shall therefore overview the problems of set theory, the various solutions and assess the influence on nominalisation. We shall then discuss Aczel's Frege structures and compare them with Scott domains. Moreover, ..."
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This paper argues that the basic problems of nominalisation are those of set theory. We shall therefore overview the problems of set theory, the various solutions and assess the influence on nominalisation. We shall then discuss Aczel's Frege structures and compare them with Scott domains. Moreover, we shall set the ground for the second part which demonstrates that Frege structures are a suitable framework for dealing with nominalisation. Keywords: Frege structures, Nominalisation, Logic and Type freeness. 1 The Problems We shall examine the problem of the semantics of nominalised terms from two angles: the formal theory and the existence of models. 1.1 The problem of the formal theory Any theory of nominalisation should be accompanied by some ontological views on concepts  for predicates and open wellformed formulae act semantically as concepts. This is vague, however, if only because where I use the word concept, someone else might use class, predicate, set, property or even...
Set Theory and Nominalisation, Part II
 Journal of Logic and Computation
, 1992
"... In this paper we shall meet the application of Scott domains to nominalisation and explain its problem of predication. We claim that it is not possible to find a solution to such a problem within semantic domains without logic. Frege structures are more conclusive than a solution to domain equations ..."
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In this paper we shall meet the application of Scott domains to nominalisation and explain its problem of predication. We claim that it is not possible to find a solution to such a problem within semantic domains without logic. Frege structures are more conclusive than a solution to domain equations and can be used as models for nominalisation. Hence we develop a type theory based on Frege structures and use it as a theory of nominalisation. Keywords: Frege structures, Nominalisation, Logic and Type freeness. 1 Frege structures, a formal introduction Having in part I informally introduced Frege structures, I shall here fill in all the technical details and show that Frege structures exist. Consider F 0 , F 1 ; : : : ; a family F of collections where F 0 is a collection of objects, and (8n ? 0)[F n is a collection of nary functions from F n 0 to F 0 ]. Definition 1.1 (An explicitly closed family) A family F as above is explicitly closed iff: For every expression e[x 1 ; : : : ; x n...
Nominalization, Predication and Type Containment
, 1993
"... In an attempt to accommodate natural language phenomena involving nominalization and selfapplication, various researchers in formal semantics have proposed abandoning the hierarchical type system which Montague inherited from Russell, in favour of more flexible type regimes. We briey review the mai ..."
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In an attempt to accommodate natural language phenomena involving nominalization and selfapplication, various researchers in formal semantics have proposed abandoning the hierarchical type system which Montague inherited from Russell, in favour of more flexible type regimes. We briey review the main extant proposals, and then develop a new approach, based semantically on Aczel's notion of Frege structure, which implements a version of subsumption polymorphism. Nominalization is achieved by virtue of the fact that the types of predicative and propositional complements are contained in the type of individuals. Russell's paradox is avoided by placing a typeconstraint on lambdaabstraction, rather than by restricting comprehension.
Reasoning about Knowledge and Belief: A Syntactical Treatment
 Logical Journal of the IGPL
, 2002
"... The study of formal theories of agents has intensified over the last couple of decades, since such formalisms can be viewed as providing the specifications for building rational agents and multiagent systems. Most of the proposed approaches are based upon the wellunderstood framework of modal logi ..."
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The study of formal theories of agents has intensified over the last couple of decades, since such formalisms can be viewed as providing the specifications for building rational agents and multiagent systems. Most of the proposed approaches are based upon the wellunderstood framework of modal logics and possible world semantics. Although intuitive and expressive, these approaches lack two properties that can be considered important to a rational agent's reasoning: quantification over the propositional attitudes, and selfreferential statements. This paper presents an alternative framework which is different from those found in the literature in two ways: Firstly, a syntactical approach for the representation of the propositional attitudes is adopted. This involves the use of a truth predicate and syntactic modalities which are defined in terms of the truth predicate itself and corresponding modal operators. Secondly, an agent's information state includes both knowledge and beliefs. Independent modal operators for the two notions are introduced and based on them syntactic modalities are defined. Furthermore, the relation between knowledge and belief is thoroughly explored and three different connection axiomatisations for the modalities and the syntactic modalities are proposed and their properties investigated.