There are two ways of incorporating temporal distinctions into a system of logic: tensed theories propose to expand standard logic with intensional tense operators; tenseless theories try to make do with the resources of extensional first-order logic, by using quantification over suitably chosen temporal entities, such as metaphysically basic time points or temporal parts. My concern in this pa...

Le programme d'analyse~ dont nous allons d~finir ici une partie, fait partie d'un programme de traduction automatique de l'allemand en d'autres langues choisies ~ volont~. Nous prendrons pour base une forme du programme id~alis~e, qui sans consideration de la capacit~'limit~e de l'ordinateur explique toutes les differences des constructions allemandes entre elles. De cette mani~re on dolt regar...

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...

The aggregation of consistent individual judgments on logically interconnected propositions into a collective judgment on the same propositions has recently drawn much attention. Seemingly reasonable aggregation procedures, such as propositionwise majority voting, cannot ensure an equally consistent collective conclusion. The literature on judgment aggregation refers to such a problem as the di...

Deduction Modulo implements Poincaré’s principle by identifying deduction and computation as different paradigms and making their interaction possible. This leads to logical systems like the sequent calculus or natural deduction modulo. Even if deduction modulo is logically equivalent to first-order logic, proofs in such systems are quite different and dramatically simpler with one cost: cut el...

Traditional methods of computing standardized mortality ratios (SMR) in mortality studies rely upon a number of conventional statistical propositions to estimate confidence intervals for obtained values. Those propositions include a common but arbitrary choice of the confidence level and the assumption that observed number of deaths in the test sample is a purely random quantity. The latter ass...

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...