Online research in philosophy

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)

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.