the topic of “trilogical denotations” (al-dalalat al-thalath) appears in avicenna logic system following the development of the discourse on “terms subject” (al-mabahith al-alfad) in his system. it was avicenna, who, for the first time, paid more attention to this subject and was responsible for its extended discussion. among the issues to which he addresses is the one on trilogical denotations...

This paper discusses certain problems arising within the treatment of the senses of functions in Alonzo Church’s Logic of Sense and Denotation. Church understands such senses themselves to be “sense-functions,” functions from sense to sense. However, the conditions he lays out under which a sense-function is to be regarded as a sense presenting another function as denotation allow for certain u...

The modal logic S4 can be used via a Curry-Howard style correspondence to obtain a λcalculus. Modal (boxed) types are intuitively interpreted as ‘closed syntax of the calculus’. This λ-calculus is called modal type theory — this is the basic case of a more general contextual modal type theory, or CMTT. CMTT has never been given a denotational semantics in which modal types are given denotation ...

Session types are used to describe and structure interactions between independent processes in distributed systems. Higher-order types are needed in order to properly structure delegation of responsibility between processes. In this paper we show that higher-order web-service contracts can be used to provide a fully-abstract model of recursive higher-order session types. The model is settheoret...

We present an algorithm for computing directly the denotation of a modal μcalculus formula χ with backwards modalities over the configuration graph of a pushdown system. Our method gives the first extension of the saturation technique to the full modal μ-calculus with backwards modalities. Finite word automata are used to represent sets of pushdown configurations. Starting from an initial autom...

In this paper, I provide an account of scientific representation that makes sense of the notion both at the nanoscale and at the quantum level: the partial mappings account. The account offers an extension of a proposal developed by R. I. G. Hughes in terms of denotation, demonstration, and interpretation (DDI). I first argue that the DDI account needs some amendments to accommodate representat...

The paper discusses a prominent one of Kratzer’s (1986, 1991, 2012) arguments against material implication analyses the denotation (indicative) conditional sentences. This is argument based on sentence Most time, if man buys horse, he pays cash for it. It shown that makes prediction does conform to speakers’ intuitions, contrary claim. also argues Lewis’s (1975) attack sentences examples where ...

The modal logic S4 can be used via a Curry-Howard style correspondence to obtain a λcalculus. Modal (boxed) types are intuitively interpreted as ‘closed syntax of the calculus’. This λ-calculus is called modal type theory — this is the basic case of a more general contextual modal type theory, or CMTT. CMTT has never been given a denotational semantics in which modal types are given denotation ...

Kripke’s solution to the Liar Paradox and other paradoxes of truth (1975) is generalized to the paradoxes of denotation. Berry’s Paradox and Hilbert and Bernays’ Paradox are treated in detail.