Combinatory Categorial Grammar is a generalization of classical Categorial Grammar that is at the least greater level of expressive power than context-free grammar that has yet been identified. The paper reviews its use for the explanatory analysis of natural language grammar, particularly with respect to bounded and unbounded constructions, multiple dependencies, relativization, and coordination.

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Logics and languages

Combinatory Categorial Grammar

One of the great strengths of public-key cryptography is its potential to allow the localization of trust. This potential is greatest when cryptography is present to guarantee data integrity rather than secrecy, and where there is no natural hierarchy of trust. Both these conditions are typically fulfilled in the commercial world, where CSCW requires sharing of data and resources across organizational boundaries. One property which trust is frequently assumed or “proved” to have is transitivity (if A trusts B and B trusts C then A trusts C) or some generalization of transitivity such as *-closure. We use the loose term unintensional transitivity of trust to refer to a situation where B can effectively put things into A's set of trust assumptions without A's explicit consent (or sometimes even awareness.) Any account of trust which allows such situations to arise clearly poses major obstacles to the effective confinement (localization) of trust. In this position paper, we argue against the need to accept unintensional transitivity of trust. We distinguish the notion of trust from a number of other (transitive) notions with which it is frequently confused, and argue that “proofs” of the unintensional transitivity of trust typically involve unpalatable logical assumptions as well as undesirable consequences.

/pdf/why-isn-t-trust-transitive-40u4aaes8k.pdf

Why Isn't Trust Transitive?

This is a survey of the origins of mathematical interpretations of modal logics, and their development over the last century or so. It focuses on the interconnections between algebraic semantics using Boolean algebras with operators and relational semantics using structures often called Kripke models. It reviews the ideas of a number of people who independently contributed to the emergence of relational semantics, and compares them with the work of Kripke. It concludes with an account of several applications of modal model theory to mathematics and theoretical computer science.

background

Mathematical modal logic: A view of its evolution

The Principle of Semantic Compositionality (sometimes called ‘Frege's Principle’) is the principle that the meaning of a (syntactically complex) whole is a function only of the meanings of its (syntactic) parts together with the manner in which these parts were combined. This principle has been extremely influential throughout the history of formal semantics; it has had a tremendous impact upon modern linguistics ever since Montague Grammars became known; and it has more recently shown up as a guiding principle for a certain direction in cognitive science. Despite the fact that The Principle is vague or underspecified at a number of points — such as what meaning is, what counts as a part, what counts as a syntactic complex, what counts as combination — this has not stopped some people from viewing The Principle as obviously true, true almost by definition. And it has not stopped other people from viewing The Principle as false, almost pernicious in its effect. And some of these latter theorists think that it is an empirically false principle while others think of it as a methodologically wrong-headed way to proceed. In fact, there are approximately 318 arguments against The Principle which can be found in the literature, whereas there are only three (or maybe four) arguments proposed in favor of The Principle. This paper will adjudicate among these arguments. And at the end it will suggest some other way to look at what proponents of compositionality really want.

/pdf/the-principle-of-semantic-compositionality-4r89poegcj.pdf

Logics and languages

Citations

Combinatory Categorial Grammar

Why Isn't Trust Transitive?

Mathematical modal logic: A view of its evolution

The Principle of Semantic Compositionality

Towards a referential analysis of temporal expressions

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