The semantic paradoxes, whose paradigm is the Liar, played a crucial role at a crucial juncture in the development of modern logic. In his 1908 seminal paper, Russell outlined a system, soon to become that of the Principia Mathematicae, whose main goal was the solution of the logical paradoxes, both semantic and settheoretic. Russell did not distinguish between the two and his theory of types w...

Section 1 discusses properties and propositions, and some of the motivation for an account in which property instantiation and propositional truth behave naively . Section 2 generalizes a standard Kripke construction for naive properties and propositions, in a language with modal operators but no conditionals. Whereas Kripke uses a 3-valued value space, the generalized account allows for a broa...

Image factorizations in regular categories are stable under pullbacks, so they model a natural modal operator in dependent type theory. This unary type constructor [A] has turned up previously in a syntactic form as a way of erasing computational content, and formalizing a notion of proof irrelevance. Indeed, semantically, the notion of a support is sometimes used as surrogate proposition asser...

Ambiguous propositions are analyzed in a type system where disambiguation is effected during assembly (i.e. by coercion). Ambiguity is introduced through a layer of types that are underspecified relative to a pre-existing collection of dependent types, construed as unambiguous propositions. A simple system of reasoning directly with such underspecification is described, and shown to be sound an...

This paper uses possible-world semantics to model the changes that may occur in an agent’s knowledge as she loses information. This builds on previous work in which the agent may forget the truth-value of an atomic proposition, to a more general case where she may forget the truth-value of a propositional formula. The generalization poses some challenges, since in order to forget whether a comp...

Dear Hans-Jörg! In the seventies and early eighties we have been colleagues in the ‘Automatentheorie und Formale Sprachen’ group at TU Berlin and shared many interests. Later we departed into different fields of research and followed different directions of thought. It is thirty years now that we have completed our PhD at TU Berlin, and this year is your sixtieth birthday. Since the times at AT...

The event template for a verb is a lexical representation of the type of event that the verb can denote. Manner of motion verbs have a simple template: An entity is engaged in a manner of motion activity (e.g., walk). Change of location verbs have a different template: An entity changes from one location to another (e.g., arrive). We propose, and support empirically, that these templates determ...

This paper discusses some structural conditions under which Russellian propositions in the sense of J. Barwise and J. Etchemendy [2] are paradoxical, and the computational complexity of the problems whether or not Russellian proposition is paradoxical, intrinsically paradoxical, and classical.