Showing papers by "Neil Tennant published in 1994"
TL;DR: This paper proposes a ‘staining algorithm’ which identifies which sentences to reject when contracting a theory, and investigates how one can nevertheless characterize contraction in a theoretically fruitful way.
Abstract: The theory of theory change has contraction and revision as its central notions. Of these, contraction is the more fundamental. The best-known theory, due to Alchourr6n, Gdirdenfors, and Makinson, is based on a few central postulates. The most fundamental of these is the principle of recovery: if one contracts a theory with respect to a sentence, and then adds that sentence back again, one recovers the whole theory. Recovery is demonstrably false. This paper shows why, and investigates how one can nevertheless characterize contraction in a theoretically fruitful way. The theory proposed lends itself to implementation, which in turn could yield new theoretical insights. The main proposal is a 'staining algorithm' which identifies which sentences to reject when contracting a theory. The algorithm requires one to be clear about the structure of reasons one has for including sentences within one's theory.
17 citations
TL;DR: In this paper, the authors define a system IR of first-order intuitionistic relevant logic, which allows one to prove every intuitionistic consequence of any consistent set of premisses.
Abstract: We define a system IR of first-order intuitionistic relevant logic. We show that intuitionistic mathematics (on the assumption that it is consistent) can be relevantized, by virtue of the following metatheorem: any intuitionistic proof of A from a setX of premisses can be converted into a proof in IR of eitherA or absurdity from some subset ofX. Thus IR establishes the same inconsistencies and theorems as intuitionistic logic, and allows one to prove every intuitionistic consequence of any consistent set of premisses.
9 citations
01 Jan 1994
TL;DR: This article re-applied the distinctions between analytic and synthetic and betweena priori and aposteriori (paceQuine) to answer these questions in what they hope is a novel and interesting way.
Abstract: What would a satisfying neo-Kantian and neo-Quinean account of logic be like? How should we account for its role as an instrument for acquiring knowledge, and as an instrument for the criticism of theories? How should we account for its special status in the epistemic scheme of things? I intend below to re-apply the distinctions between analytic and synthetic and betweena prioriand aposteriori (paceQuine) to answer these questions in what I hope is a novel and interesting way. My answers will put me at odds with both Kantians and Quineans; for I do not think that avoiding disagreements with either camp puts one wholly in the other.
3 citations
TL;DR: In this paper, Milne's counterexample is used to save the situation in the light of the conjecture in the sense that every sequent provable in the system IR of intuitionistic relevant logic is a substitution instance of an intuitionistic valid sequent that has no intuitionistically valid proper subsequent.
Abstract: Peter Milne (this issue, [1]) has produced a neat counterexample to my conjecture in [2] that every sequent provable in the system IR of intuitionistic relevant logic is a substitution instance of an intuitionistically valid sequent that has no intuitionistically valid proper subsequent. While the Popperian in me rejoices, the relevantist/intuitionist in me might have to resign itself with disappointment to the prospect that the conjecture might not hold for any system worthy of the title of intuitionistic relevant logic. Now while I do not think the truth of the conjecture is essential to IR, it would still be welcome if it were so. What, then, can be done to save the situation in the light of Milne's counterexample? The sequent that Milne provides as his counterexample is A v B, A, B : A & B and its proof in IR is as follows:1 (1) -(1) (0) A B A B AvB A&B A&B A&B Let us recall the guiding idea behind the treatment of relevance embodied in the systems CR and IR. The main aim was to avoid thinning, or dilution structural inferences (in a sequent system) that become sources of irrelevant connections between sets of premisses and conclusions drawn from them. The slogan here could be:
3 citations