1. KNOWLEDGE BY INFERENCE I believe many things, but I also know I’m wrong about some of them. There is nothing irrational, bad, or paradoxical about my epistemic situation. In fact, it seems that there’s something wrong with subjects who don’t know, or at least strongly believe, that they are mistaken about one or more of their beliefs. This mundane and seemingly innocent observation, nonethel...

Gentzen’s and Jaśkowski’s formulations of natural deduction are logically equivalent in the normal sense of those words. However, Gentzen’s formulation more straightforwardly lends itself both to a normalization theorem and to a theory of “meaning” for connectives (which leads to a view of semantics called ‘inferentialism’). The present paper investigates cases where Jaskowski’s formulation see...

On the one hand, hierarchical organizations are rigid in the sense that there is only one path to each document. On the other hand, keyword-based search is flexible because many sets of keywords may lead to the same document, but it lacks a navigation mechanism. We present the new paradigm of a logic file system, which integrates navigation and classification, and the possibility of expressive ...

According to a main idea of Gentzen the meanings of the logical constants are reflected by the introduction rules in his system of natural deduction. This idea is here understood as saying roughly that a closed argument ending with an introduction is valid provided that its immediate subarguments are valid and that other closed arguments are justified to the extent that they can be brought to i...

We present a theoretical and practical approach to the modular natural deduction presentation of modal logics and their implementation in a logical framework. Our work treats a large and well-known class of modal logics (including K, D, T , B, S4, S4:2, KD45, S5) in a uniform way with respect to soundness and completeness for semantics, and faithfulness and adequacy of the implementation. Moreo...

We investigate several fragments of multiplicative linear logic, in a natural deduction setting and with the aim of a better understanding of the par connective. We study, first, a pre-tensorial calculus, which is strengthened then in the standard tensorial fragment. The addition of a further pre-tensorial connective yields (a natural deduction version of) Full Intuitionistic Linear Logic. A fu...

This paper presents a simple logical framework for default reasoning. The semantics is normal first order model theory; instead of changing the logic, the way in which the logic is used is changed. Rather than expecting reasoning to be just deduction (in any logic) from our knowledge, we examine the consequences of viewing reasoning as a very simple case of theory formation. By treating default...

We present a theoretical and practical approach to the modular natural deduction presentation of modal logics and their implementation in a logical framework. Our work treats a large and well-known class of modal logics (including K, D, T, B, S4, S4:2, KD45, S5) in a uniform way with respect to soundness and completeness for semantics, and faith-fulness and adequacy of the implementation. Moreo...

Proof-theory has traditionally been developed based on linguistic (symbolic) representations of logical proofs. Recently, however, logical reasoning based on diagrammatic or graphical representations has been investigated by logicians. Euler diagrams were introduced in the 18th century by Euler [1768]. But it is quite recent (more precisely, in the 1990s) that logicians started to study them fr...

We propose a new framework for representing logics, called LF + and based on the Ed-inburgh Logical Framework. The new framework allows us to give, apparently for the rst time, general deenitions which capture how well a logic has been represented. These deen-itions are possible since we are able to distinguish in a generic way that part of the LF + entailment which corresponds to the underlyin...