Raymond Turner

Semantics and property theory

The nature of properties, relations and propositions has always been at the heart of philosophical debate. Among other things, they have played a central role in theories of intensionality, belief, universals and in the analysis of the attitudes. In fact, it does not seem unwarranted to claim that most of the entities that populate philosophical debates are ulti mately analyzable through constructs which crucially rely upon proper ties and propositions. The aim of this paper is to develop a theory of properties, relations and propositions which will support, in a strong sense, the semantics of natural language. By that we mean that a semantics built on such a theory of properties should mesh well with (what is known about) syntax, help explaining why predicative expressions in English and other lan guages behave the way they do, and constitute, on this score, an improvement over purely set-theoretic semantics (such as, e.g., Mon

A Theory of Properties

Freges attempts to formulate a theory of properties to serve as a foundation for logic, mathematics and semantics all dissolved under the weight of the logicial paradoxes. The language of Freges theory permitted the representation of the property which holds of everything which does not hold of itself. Minimal logic, plus Freges principle of abstraction, leads immediately to a contradiction. The subsequent history of foundational studies was dominated by attempts to formulate theories of properties and sets which would not succumb to the Russell argument. Among such are Russells simple theory of types and the development of various iterative conceptions of set. All of these theories ban, in one way or another, the self-reference responsible for the paradoxes; in this sense they are all “typed” theories. The semantical paradoxes, involving the concept of truth, induced similar nightmares among philosophers and logicians involved in semantic theory. The early work of Tarski demonstrated that no language that contained enough formal machinery to respresent the various versions of the Liar could contain a truth-predicate satisfying all the Tarski biconditionals. However, recent work in both disciplines has led to a re-evaluation of the limitations imposed by the paradoxes. In the foundations of set theory, the work of Gilmore [1974], Feferman [1975], [1979], [1984], and Aczel [1980] has clearly demonstrated that elegant and useful type-free theories of classes are feasible. Work on the semantic paradoxes was given new life by Kripkes contribution (Kripke [1975]). This inspired the recent work of Gupta [1982] and Herzberger [1982]. These papers demonstrate that much room is available for the development of theories of truth which meet almost all of Tarskis desiderata.

The Philosophy of Computer Science

The Philosophy of Computer Science is concerned with those philo-sophical issues that surround and underpin the academic discipline of computer science. In this paper we provide an introduction to some itsphilosophical concerns.

YPA — an Intelligent Directory Enquiry Assistant

The YPA project is building a system to make the information in classified directories more accessible. BTs Yellow Pages®1 provides an example of classified database with which this work would be useful.There are two reasons for doing this: (i) directories like Yellow Pages contain much useful but hard-to-access information, especially in the free text in semi-display advertisements; (ii) more generally, the project is a demonstrator for exploitation of semi-structured data — data that is less systematic than database entries or logical clauses, but more systematic than free text because it has been marked up, for display or some other purpose.Accessing the directory source data file requires both natural language processing (for softening the interface to the system, and separately for analysis of natural-language-like constructs in the data) and information retrieval techniques, which are assisted by shallow knowledge. Deep world knowledge is impractical.The project seeks to get maximum effect from conveniently simplified approximations of standard natural language processing and knowledge representation. The paper gives an overview of the system, and illustrates its style with points about how the source data file is analysed. The YPA requires further development, but already demonstrates the effectiveness of shallow processing applied to semi-structured data.

The Foundations of Specification

We develop and explore a Core Specification Theory(CST) as a basis for the meta-mathematical investigation of specification and specification languages.

Computable Models

We investigate mathematical modelling with theories of data types. We provide a formal setting for the formulation of such theories (TPL) and use it to introduce the notion of a computational model. We explore the notion and provide several case studies.

A Constructive Set Theory for Program Development

We present a constructive theory of types and kinds (called TK5) designed with program development as the major desideratum. We motivate its definition with respect to existing research in the area of program logics (in particular Martin-Lofs theory of types) and establish suitable infrastructure for program extraction from proofs of specifications.

Counterfactuals without possible worlds

is true exactly when JI is derivable from 4 together with a suitable set of sentences S. Intuitively, S is to consist of sentences which (i) are in fact true and (ii) would also have been true, if contrary to fact,

Understanding Programming Languages

had been true. The second condition, which is strictly speaking a condition on S as a whole, Goodman referred to as the contenability of S with 4. The problem with (ii) as it stands is that it involves a counterfactual construction; any such account for the truthconditions of counterfactuals must, therefore, be circular. Furthermore, there does not appear to be a simple alternative characterisation of cotenability which is free from counterfactual constructions. Goodman himself thought that the only possible way to escape from this circularity would be to account for the truth-conditions of counterfactuals in terms of underlying natural laws; and a theory of lawlikeness which would include a solution of his socalled projection problem. Unfortunately, as Goodman himself emphasises, this would destroy his original claim to explicate the concept of law by reference to counterfactuals. Worse still, it now appears that the projection problem, which Goodman subsequently cameto see as the kernel of the problem of lawlikeness, can in its turn only be solved if we appeal to certain laws. Bob Stalnaker and David Lewis independently developed theories which, although they do not solve completely the problem of truth-conditions, say enough about it to clarify to a large extent the logic of conditionals. Stalnaker supposes that the circumstances in which we use a conditional (1) determine a function (f, say) which maps sentences onto alternative situations in which the sentences are true. The conditional (1) is true in

Extracting Semistructured Data - Lessons Learnt

We document the influence on programming language semantics of the Platonism/formalism divide in the philosophy of mathematics.