Related papers: Another Combination of Classical and Intuitionisti…

We generalize intuitionistic tense logics to the multi-modal case by placing grammar logics on an intuitionistic footing. We provide axiomatizations for a class of base intuitionistic grammar logics as well as provide axiomatizations for…

We propose two new dependent type systems. The first, is a dependent graded/linear type system where a graded dependent type system is connected via modal operators to a linear type system in the style of Linear/Non-linear logic. We then…

Canonical expressions are representative of implicative propositions upto renaming of variables. In this paper we explore, using a Monte-Carlo approach, the model of canonical expressions in order to confirm the paradox that says that…

We develop a framework for epistemic logic that combines relevant modal logic with classical propositional logic. In our framework the agent is modeled as reasoning in accordance with a relevant modal logic while the propositional fragment…

This report first shows the equivalence bewteen several formulations of classical logic in intuitionistic logic (tertium non datur, reductio ad absurdum, Pierce's law). Then it establishes the correctness of the G\"odel-Kolmogorov…

We introduce a basic intuitionistic conditional logic $\mathsf{IntCK}$ that we show to be complete both relative to a special type of Kripke models and relative to a standard translation into first-order intuitionistic logic. We show that…

The quantum logical `or' is analyzed from a physical perspective. We show that it is the existence of EPR-like correlation states for the quantum mechanical entity under consideration that make it nonequivalent to the classical situation.…

This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…

We present two deductively equivalent calculi for non-deterministic many-valued logics. One is defined by axioms and the other - by rules of inference. The two calculi are obtained from the truth tables of the logic under consideration in a…

We combine the concepts of modal logics and many-valued logics in a general and comprehensive way. Namely, given any finite linearly ordered set of truth values and any set of propositional connectives defined by truth tables, we define the…

With help of a compact Prolog-based theorem prover for Intuitionistic Propositional Logic, we synthesize minimal assumptions under which a given formula formula becomes a theorem. After applying our synthesis algorithm to cover basic…

We define a model for linear logic based on two well-known ingredients: games and simulations. This model is interesting in the following respect: while it is obvious that the objects interpreting formulas are games and that everything is…

Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the top-level logical symbol of that formula. We…

Nonmonotonic logics are usually characterized by the presence of some notion of 'conditional' that fails monotonicity. Research on nonmonotonic logics is therefore largely concerned with the defeasibility of argument forms and the…

A sound and complete embedding of conditional logics into classical higher-order logic is presented. This embedding enables the application of off-the-shelf higher-order automated theorem provers and model finders for reasoning within and…

Intuitionistic grammar logics fuse constructive and multi-modal reasoning while permitting the use of converse modalities, serving as a generalization of standard intuitionistic modal logics. In this paper, we provide definitions of these…

When a physicist performs a quantic measurement, new information about the system at hand is gathered. This paper studies the logical properties of how this new information is combined with previous information. It presents Quantum Logic as…

The notion of a non-deterministic logical matrix (where connectives are interpreted as multi-functions) extends the traditional semantics for propositional logics based on logical matrices (where connectives are interpreted as functions).…

In the philosophical tradition of `analytic pragmatism', which attempts to account for linguistic meanings in terms of their practices of use, logical expressivism is a theory which offers a distinct perspective on logic. We shed light on…

There is knowledge. There is belief. And there is tacit agreement.' 'We may talk about objects. We may talk about attributes of the objects. Or we may talk both about objects and their attributes.' This work inspects tacit agreements on…