We develop a principled integration of shared mutable state into proposition-as-types linear logic interpretation session-based concurrent programming language. While the foundation type systems for functional core languages often builds on correspondence, automatically ensuring strong safety and liveness properties, imperative features have mostly been handled by extra-logical constructions. O...

In this paper I will focus on the question of what theoretical object we should use to represent the meaning of certain sentences. In particular, I will focus on the question of whether we should use propositions to represent the meaning of indicative conditionals. Before getting into this question I’ll try to locate it in the broader scheme of things. In recent years, the so-called semantic/pr...

The authors provide an object-theoretic analysis of two paradoxes in the theory of possible worlds and propositions stemming from Russell and Kaplan. After laying out the paradoxes, the authors provide a brief overview of object theory and point out how syntactic restrictions that prevent object-theoretic versions of the classical paradoxes are justified philosophically. The authors then trace ...

The idea that temporal propositions are vague predicates is examined with attention to the nature of the objects over which the predicates range. These objects should not, it is argued, be identified once and for all with points or intervals in the real line (or any fixed linear order). Context has an important role to play not only in sidestepping the Sorites paradox (Gaifman 2002) but also in...

We present a new parametricity translation for a significant fragment of Coq. Previous translations of parametrically polymorphic propositions allowed nonuniformity. For example, on related instantiations, a function may return propositions that are logically inequivalent (e.g. T rue and False). We show that uniformity of polymorphic propositions is not achievable in general. Nevertheless, our ...