There are simple, purely syntactic axiomatic proof systems for both the logical truths and the logical falsehoods of propositional logic. However, to date no such system has been developed for the logical contingencies, that is, formulas that are both satisfiable and falsifiable. This paper formalizes and purely syntactic axiomatic proof systems for the logical contingencies and proves its soun...

How can we explain why we should ascribe some logical properties to an agent’s preferences, and why we should not ascribe others to them? Although this problem is very important, little attention has been given to it. We break this problem down into the three: Problem 1. When we attempt to ascribe some logical properties to the preferences of an agent, how can we explain this ascription? Proble...

This paper presents a novel syntactic logical relation for a polymorphic linear λ-calculus that treats all types as linear and introduces the constructor ! to account for intuitionistic terms, and System F◦—an extension of System F that uses kinds to distinguish linear from intuitionistic types. We define a logical relation for open values under both open linear and intuitionistic contexts, the...

Intuitionism can be seen as a verificationism restricted to mathematical discourse. An attempt to generalize intuitionism to empirical discourse presents various challenges. One of those concerns the logical and semantical behavior of what has been called ‘empirical negation’. An extension of intuitionistic logic with empirical negation was given by Michael De and a labelled tableaux system was...

This paper considers Reynolds’s separation logic with all logical connectives but without arbitrary predicates. This logic is not recursively enumerable but is very useful in practice. We give a sound labelled sequent calculus for this logic. Using numerous examples, we illustrate the subtle deficiencies of several existing proof calculi for separation logic, and show that our rules repair thes...

A growing number of mobile computing applications is centered around the user’s location. The notion of location is broad, ranging from physical coordinates (latitude/longitude) to logical locations (like Starbucks). While extensive research has been performed in physical localization, there has been far fewer attempts in recognizing logical places. This paper argues that the increasing number ...

We introduce a multimodal stratified framework MS that generalizes an idea hidden in the definitions of Light Linear/Affine logical systems: “More modalities means more expressiveness”. MS is a set of building-rule schemes that depend on parameters.We interpret the values of the parameters as modalities. Fixing the parameters yields deductive systems as instances of MS, that we call subsystems....

Three recent demands on quantifier scoping algorithms have been that they should be explicitly stated, they should be sound and complete with respect to the input sentence [Hobbs and Shieber 1987] and they should not employ a 'Free Variable Constraint' [Pereira 1989]. The first demand is for good academic practice. The second is to ask for an algorithm that generates all and only the possible s...