What explains the truth of a universal generalization? Two types explanation can be distinguished. While an ‘instance-based explanation’ proceeds via some or all instances generalization, ‘generic is independent instances, relying instead on completely general facts about properties operations involved in generalization. This intuitive distinction analyzed by means truthmaker semantics, which a...

We investigate a non-classical version of linear temporal logic whose propositional fragment is Gödel–Dummett (which well known both as superintuitionistic and t-norm fuzzy logic). define the using two natural semantics, real-valued semantics bi-relational show that these indeed one same logic. Although this Gödel does not have any form finite model property for we every falsifiable formula on ...

In a recent paper, Jean-Yves Girard commented that ”it has been a long time since philosophy has stopped intereacting with logic”[17]. Actually, it has not been such a ”long” time since, e.g., Dag Prawitz and Michael Dummett developed philosophical arguments within the paradigm of Gentzen-style systems in favour of the adoption of intuitionistic logic. But recent developments within logic have ...

. 1 Preliminaries Consider the variety Eω generated by the algebra ω := (N, ·), where i · j := max (i, j) for i 6= j, and i · j := 1 for i = j, i, j ∈ N1. These variety is a subvariety of the variety of equivalential algebras E . By an equivalential algebra we mean a grupoid A = (A,↔) that is a subreduct of a Brouwerian semilattice (or, equivalently, a Heyting algebra) with the operation ↔ give...

In this paper we present a multiple premise tableau calculus for propositional Dummett Logic. The aim is to improve the efficiency of the known decision procedures. The investigation is related to the possibility of reducing the size of the deduction by the replacement rule and rules that introduce formulas equivalent to the logical constant True. In this way we want to bound the application of...

Quantified propositional intuitionistic logic is obtained from propositional intuitionistic logic by adding quantifiers ∀p, ∃p, where the propositional variables range over upward-closed subsets of the set of worlds in a Kripke structure. If the permitted accessibility relations are arbitrary partial orders, the resulting logic is known to be recursively isomorphic to full second-order logic (K...

The standard approach to what I call “proof-theoretic semantics”, which is mainly due to Dummett and Prawitz, attempts to give a semantics of proofs by defining what counts as a valid proof. After a discussion of the general aims of proof-theoretic semantics, this paper investigates in detail various notions of prooftheoretic validity and offers certain improvements of the definitions given by ...

We present an algorithm for deciding Gödel-Dummett logic. The originality of this algorithm comes from the combination of proofsearch in sequent calculus, which reduces a sequent to a set of pseudoatomic sequents, and counter-model construction of such pseudo-atomic sequents by a fixpoint computation. From an analysis of this construction, we deduce a new logical rule [⊃N ] which provides short...