This paper considers the computational complexity of the disjunc-tion and existential properties of intuitionistic logic. We prove that the disjunction property holds feasibly for intuitionistic propositional logic; i.e., from a proof of A _ B, a proof either of A or of B can be found in polynomial time. For intuitionistic predicate logic, we prove superexponential lower bounds for the disjunct...

Sergei Artemov Reflection vs. co-Reflection in Intuitionistic Epistemic Logic. This is joint work with Tudor Protopopescu. We outline an intuitionistic view of knowledge which maintains the Brouwer-Heyting-Kolmogorov semantics and is consistent with Williamson’s suggestion that intuitionistic knowledge is the result of verification. On this view, co-Reflection F → KF is valid since it encodes a...

We propose a new bi-intuitionistic type theory called Dualized Type The-ory (DTT). It is a simple type theory with perfect intuitionistic duality, and correspondsto a single-sided polarized sequent calculus. We prove DTT strongly normalizing, andprove type preservation. DTT is based on a new propositional bi-intuitionistic logic calledDualized Intuitionistic Logic (DIL) that bui...

This paper proposes a new syntax and proof system called Dualized Intuitionistic Logic (DIL), for intuitionistic propositional logic with the subtraction operator. Our goal is a conservative extension of standard propositional intuitionistic logic with perfect duality (symmetry) between positive and negative connectives. The proof system should satisfy the following metatheoretic properties: so...

We introduce logic-enriched intuitionistic type theories, that extend intuitionistic dependent type theories with primitive judgements to express logic. By adding type theoretic rules that correspond to the collection axiom schemes of the constructive set theory CZF we obtain a generalisation of the type theoretic interpretation of CZF. Suitable logic-enriched type theories allow also the study...

In this paper we define a Intuitionistic Conditional Logic for Access Control (CCAC ). The logic is based on a conditional language allowing principals to be defined as arbitrary formulas. CCAC is a intuitionistic conditional logic, which includes few uncontroversial axioms of access control logics. The paper provides an axiomatization and a Kripke model semantics for the logic CCAC and proves ...

We present a new intuitionistic linear logic, Dual Intuitionistic Linear Logic, designed to reflect the motivation of exponentials as translations of intuitionistic types, and provide it with a term calculus, proving associated standard type-theoretic results. We give a sound and complete categorical semantics for the type-system, and consider the relationship of the new type-theory to the more...

The logic of bunched implication BI provides a framework for reasoning about resource composition and forms the basis for an assertion language of separation logic which is used to reason about software programs. Propositional BI is obtained by freely combining propositional intuitionistic logic and multiplicative intuitionistic linear logic. It possesses an elegant proof theory: its bunched ca...

A natural deduction system for intuitionistic predicate logic with existential instantiation rule presented here uses Hilbert’s ǫ-symbol. It is conservative over intuitionistic predicate logic. We provide a completeness proof for a suitable Kripke semantics, sketch an approach to a normalization proof, survey related work and state some open problems. Our system extends intuitionistic systems w...

The logic of bunched implication BI provides a framework for reasoning about resource composition and forms the basis for an assertion language of separation logic which is used to reason about software programs. Propositional BI is obtained by freely combining propositional intuitionistic logic and multiplicative intuitionistic linear logic. It possesses an elegant proof theory: its bunched ca...