We consider a " polarized " version of bi-intuitionistic logic [9, 7, 10, 11] as a logic of assertions and hypotheses and show that it supports a " rich proof theory " and an interesting categorical interpretation, unlike the standard approach of C. Rauszer's Heyting-Brouwer logic [48, 49], whose categorical models are all partial orders by Crolard's theorem [19]. We show that P. A.Mellì es not...

Intuitionistic epistemic logic is an active research field. However, so far no consensus has been reached what the correct form of intuitionistic epistemic logic is and more technical and conceptual work is needed to obtain a better understanding. This article tries to make a small technical contribution to this enterprise. Roughly speaking, a proposition is distributed knowledge among a group ...

We introduce GIL, a new logic inspired by linear logic, focusing and polarization. GIL is a unified logic in which connectives from intuitionistic, classical and linear logic can mix with few restrictions. Systems that resemble it include Girard’s logic LU, although GIL is best considered a generalization of intuitionistic principles. Intuitionistic logic is seen as a less-complete version of G...

Issues about information spring up wherever one scratches the surface of logic. Here is a case that raises delicate issues of ‘factual’ versus ‘procedural’ information, or ‘statics’ versus ‘dynamics’. What does intuitionistic logic, perhaps the earliest source of informational and procedural thinking in contemporary logic, really tell us about information? How does its view relate to its ‘cousi...

Bi-intuitionistic logic (BINT) is a conservative extension of intuitionistic logic to include the duals of each logical connective. One leading question with respect to BINT is, what does BINT look like across the three arcs – logic, typed λ-calculi, and category theory – of the Curry-HowardLambek correspondence? Categorically, BINT can be seen as a mixing of two worlds: the first being intuiti...

This paper considers the computational complexity of the disjunction 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...

The Intuitionistic Logic Theorem Proving (ILTP) Library provides a platfom for testing and benchmarking theorem provers for first-order intuitionistic logic. It includes a collection of benchmark problems in a standardised syntax and performance results obtained by a comprehensive test of currently available intuitionistic theorem proving systems. These results are used to provide information a...

We prove that the sequent calculus LRBL for residuated basic logic RBL has strong finite model property, and that intuitionistic logic can be embedded into basic propositional logic BPL. Thus RBL is decidable. Moreover, it follows that the class of residuated basic algebras has the finite embeddability property, and that BPL is PSPACE-complete, and that intuitionistic logic can be embedded into...

This paper describes a natural deduction formulation for Full Intuitionistic Linear Logic (FILL), an intriguing variation of multiplicative linear logic, due to Hyland and de Paiva. The system FILL resembles intuitionistic logic, in that all its connectives are independent, but resembles classical logic in that its sequent-calculus formulation has intrinsic multiple conclusions. From the intrin...

Current research on non-monotonic reasoning shows growing interest on implementation details, so the need for concrete calculi formalizing non-monotonic logics is clearly recognized. On the other hand, there is also an increased number of works combining intuitionistic logic with various kinds of non-monotonic formalisms. As a case in point, intuitionistic versions of both default and autoepist...