This book is intended as a course in modal logic for students who have had prior contact
with modal logic and wish to study it more deeply. It presupposes training in mathematics or …

Refutation systems are systems of formal, syntactic derivations, designed to derive the non-
valid formulas or logical consequences of a given logic. Here we provide an overview with …

The question," Which modal logic is the right one for logical necessity?," divides into two
questions, one about model-theoretic validity, the other about proof-theoretic …

Proofs and countermodels are the two sides of completeness proofs, but, in general, failure
to find one does not automatically give the other. The limitation is encountered also for …

REFUTATION SYSTEMS IN PROPOSITIONAL LOGIC Page 1 TOMASZ SKURA REFUTATION
SYSTEMS IN PROPOSITIONAL LOGIC 1 INTRODUCTION 1.1 Basic Concepts By a refutation …

This paper introduces the category of b-frames as a new tool in the study of complete
lattices. B-frames can be seen as a generalization of posets, which play an important role in …

It is widely accepted that classical logic is trivialized in the presence of a transparent truth-
predicate. In this paper, we will explain why this point of view must be given up. The …

Bi-intuitionistic logic is the union of intuitionistic and dual intuitionistic logic, and was
introduced by Rauszer as a Hilbert calculus with algebraic and Kripke semantics. But her …

Abductive reasoning involves finding the missing premise of an “unsaturated” deductive
inference, thereby selecting a possible explanans for a conclusion based on a set of …

A novel countermodel-producing decision procedure that applies to several multi-modal
logics, both intuitionistic and classical, is presented. Based on backwards search in labeled …