The tension between expressive power and computational tractability poses an acute problem for theories of underspeciﬁed semantic representation. In previous work we have presented an account of underspeciﬁed scope representations within Property Theory with Curry Typing (PTCT), an intensional ﬁrst-order theory for natural language semantics. Here we show how ﬁlters applied to the underspeciﬁed-scope terms of PTCT permit both expressive completeness and the reduction of computational complexity in a signiﬁcant class of non-worst case scenarios.
We present Property Theory with Curry Typing (PTCT), an intensional ﬁrst-order logic for natural language semantics. PTCT permits ﬁne-grained 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 type-theoretic approach to pronominal anaphora that avoids some of the diﬃculties that undermine previous type-theoretic analyses (...) of this phenomenon. (shrink)
Intensional logic (IL) and its application to natural language, which the present monograph addresses, was ﬁrst developed by Richard Montague in the late 1960s (e.g., Montague 1970a, 1970b). Through the efforts of (especially) Barbara Partee (e.g., Partee 1975, 1976), and Richmond Thomason, who edited the posthumous collection of Montague’s works (Thomason 1974), this became the main framework for those who aspired to a formal semantic theory for natural language, and these included computational linguists as early as Jerry Hobbs in the (...) late 1970s (e.g., Hobbs and Rosenschein 1977). In fact, until the advent of the current interest in statistical linguistics with its own conception of what semantics is, IL, or some variant of it, was perhaps the main theory of semantics within computational linguistics generally. And within current computational semantics it still is. But over the years, philosophers, linguists, and computational linguists have noted a variety of shortcomings in Montague’s version of IL. Montague deﬁned intensions as functions from possible worlds to extensions in that world. But this had the effect of making logically equivalent expressions have the same intension, thus leading to the problem of “logical omniscience” (believing/knowing all the logical consequences of what is believed/known). Montague had based his IL on Church’s simple theory of types (Church 1940), supplemented with intensions of each type. But this implies that each natural language item accepts only arguments of some one ﬁxed type. However, this is not true for natural language, where conjunctions, verbs, and pretty much any functional term that accepts arguments at all can accept arguments of different types. (For example, and can accept arguments that are of the sentence type, of the verb phrase type, of the adjective type, etc.; and indeed, it can accept arguments of differing types in its different argument.. (shrink)
A BSTRACT. We present Property Theory with Curry Typing (PTCT), an intensional ﬁrst-order logic for natural language semantics. PTCT permits ﬁne-grained 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 (...) type-theoretic analyses of this phenomenon. (shrink)
In this paper we address an important issue in the development of an adequate formal theory of underspeciﬁed semantics. The tension between expressive power and computational tractability poses an acute problem for any such theory. Generating the full set of resolved scope readings from an underspeciﬁed representation produces a combinatorial explosion that undermines the eﬃciency of these representations. Moreover, Ebert (2005) shows that most current theories of underspeciﬁed semantic representation suﬀer from expressive incompleteness. In previous work we present an account (...) of underspeciﬁed scope representations within Property Theory with Curry Typing (PTCT), an intensional ﬁrst-order theory for natural language semantics. We review this account, and we show that ﬁlters applied to the underspeciﬁed-scope terms of PTCT permit expressive completeness. While they do not solve the general complexity problem, they do signiﬁcantly reduce the search space for computing the full set of resolved scope readings in non-worst cases. We explore the role of ﬁlters in achieving expressive completeness, and their relationship to the complexity involved in producing full interpretations from underspeciﬁed representations. (shrink)
The paper presents Property Theory with Curry Typing (PTCT) where the language of terms and well-formed formulæ are joined by a language of types. In addition to supporting ﬁne-grained intensionality, the basic theory is essentially ﬁrst-order, so that implementations using the theory can apply standard ﬁrst-order theorem proving techniques. The paper sketches a system of tableau rules that implement the theory. Some extensions to the type theory are discussed, including type polymorphism, which provides a useful analysis of conjunctive terms. (...) Such terms can be given a single polymorphic type that expresses the fact that they can conjoin phrases of any one type, yielding an expression of the same type. (shrink)
While a network of cortical regions contribute to face processing, the lesions in acquired prosopagnosia are highly variable, and likely result in different combinations of spared and affected regions of this network. To assess the residual functional sensitivities of spared regions in prosopagnosia, we designed a rapid event-related functional magnetic resonance imaging (fMRI) experiment that included pairs of faces with same or different identities and same or different expressions. By measuring the release from adaptation to these facial changes we determined (...) the residual sensitivity of face-selective regions-of-interest. We tested three patients with acquired prosopagnosia, and all three of these patients demonstrated residual sensitivity for facial identity changes in surviving fusiform and occipital face areas of either the right or left hemisphere, but not in the right posterior superior temporal sulcus. The patients also showed some residual capabilities for facial discrimination with normal performance on the Benton Facial Recognition Test, but impaired performance on more complex tasks of facial discrimination. We conclude that fMRI can demonstrate residual processing of facial identity in acquired prosopagnosia, that this adaptation can occur in the same structures that show similar processing in healthy subjects, and further, that this adaptation may be related to behavioral indices of face perception. (shrink)
This paper proposes a framework for formalising intuitions about the behaviour of imperative commands. It seeks to capture notions of satisfaction and coherence. Rules are proposed to express key aspects of the general logical behaviour of imperative constructions. A key objective is for the framework to allow patterns of behaviour to be described while avoiding making any commitments about how commands, and their satisfaction criteria, are to be interpreted. We consider the status of some conundrums of imperative logic in the (...) context of this proposal. (shrink)
The recent translation of Emmanuel Levinas’s essay On Escape complicates our view of his relationship to Hegel, and reopens the ontological question of escape. The impetus for Levinas’s essay was National Socialism’s effort to reduce subjectivity to being qua biologistic. To resist this, Levinas enlists idealism as an ally. He affirms the idealist subject’s effort to escape being, but denies that it makes good its escape. I challenge this denial by comparing Levinas’s phenomenology of escape with Hegel’s phenomenology of unhappy (...) consciousness, paying special attention to the themes of shame and the will to escape. The similarity between treatments leads me to suggest that the urge to escape emerges at least as early as medieval Christianity, thus predating the historical predicament of mid-1930s European Jewry. I conclude by interpreting space travel and the posthuman figure of the cyborg as signs that escape continues asan object of human aspiration. (shrink)
Religion has become a vital resource for attempts to rethink the meaning of the political. This article rehearses the efforts of two recent figures, René Girard and Giorgio Agamben, to transform the political by renewing its connection to religion. Both thinkers struggle to escape politics as defined by Carl Schmitt's friend/enemy distinction. Girard and Agamben do clash ideologically, but their inquiries into sacrifice and messianism take similar courses. Regarding origins, Girard argues for the sacrificial crisis as the common parent to (...) religion and politics. Conversely, for Agamben, the Roman figure of homo sacer distinguishes politics from religion. With respect to the future, Girard's messianism installs Christian belief as the only way to move beyond violence. By contrast, Agamben steers Pauline messianism toward the efforts to displace sovereignty and reopen the political. I conclude that Agamben breaks with Schmitt while Girard reinscribes his politics at a higher level. Key Words: Giorgio Agamben Rey Chow Christianity René Girard homo sacer messianism politics sacred sacrifice Carl Schmitt. (shrink)
This book provides a systematic study of three foundational issues in the semantics of natural language that have been relatively neglected in the past few decades. focuses on the formal characterization of intensions, the nature of an adequate type system for natural language semantics, and the formal power of the semantic representation language proposes a theory that offers a promising framework for developing a computational semantic system sufficiently expressive to capture the properties of natural language meaning while remaining computationally tractable (...) written by two leading researchers and of interest to students and researchers in formal semantics, computational linguistics, logic, artificial intelligence, and the philosophy of language. (shrink)
We present an approach to anaphora and ellipsis resolution in which pronouns and elided structures are interpreted by the dynamic identiﬁcation in discourse of type constraints on their semantic representations. The content of these conditions is recovered in context from an antecedent expression. The constraints deﬁne separation types (sub-types) in Property Theory with <span class='Hi'>Curry</span> Typing (PTCT), an expressive ﬁrst-order logic with <span class='Hi'>Curry</span> typing that we have proposed as a formal framework for natural language semantics.