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An introduction to substructural logics
, 2000
"... Abstract: This is a history of relevant and substructural logics, written for the Handbook of the History and Philosophy of Logic, edited by Dov Gabbay and John Woods. 1 1 ..."
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Cited by 140 (16 self)
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Abstract: This is a history of relevant and substructural logics, written for the Handbook of the History and Philosophy of Logic, edited by Dov Gabbay and John Woods. 1 1
A Nonstandard Approach to the Logical Omniscience Problem
 Artificial Intelligence
, 1990
"... We introduce a new approach to dealing with the wellknown logical omniscience problem in epistemic logic. Instead of taking possible worlds where each world is a model of classical propositional logic, we take possible worlds which are models of a nonstandard propositional logic we call NPL, which ..."
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Cited by 50 (4 self)
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We introduce a new approach to dealing with the wellknown logical omniscience problem in epistemic logic. Instead of taking possible worlds where each world is a model of classical propositional logic, we take possible worlds which are models of a nonstandard propositional logic we call NPL, which is somewhat related to relevance logic. This approach gives new insights into the logic of implicit and explicit'belief considered by Levesque and Lakemeyer. In particular, we show that in a precise sense agents in the structures considered by Levesque and Lakemeyer are perfect reasoners in NPL. 1
Logical Pluralism
 To appear, Special Logic issue of the Australasian Journal of Philosophy
, 2000
"... Abstract: A widespread assumption in contemporary philosophy of logic is that there is one true logic, that there is one and only one correct answer as to whether a given argument is deductively valid. In this paper we propose an alternative view, logical pluralism. According to logical pluralism th ..."
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Cited by 23 (5 self)
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Abstract: A widespread assumption in contemporary philosophy of logic is that there is one true logic, that there is one and only one correct answer as to whether a given argument is deductively valid. In this paper we propose an alternative view, logical pluralism. According to logical pluralism there is not one true logic; there are many. There is not always a single answer to the question “is this argument valid?” 1 Logic, Logics and Consequence Anyone acquainted with contemporary Logic knows that there are many socalled logics. 1 But are these logics rightly socalled? Are any of the menagerie of nonclassical logics, such as relevant logics, intuitionistic logic, paraconsistent logics or quantum logics, as deserving of the title ‘logic ’ as classical logic? On the other hand, is classical logic really as deserving of the title ‘logic ’ as relevant logic (or any of the other nonclassical logics)? If so, why so? If not, why not? Logic has a chief subject matter: Logical Consequence. The chief aim of
Carnap's Tolerance, Language Change and Logical Pluralism
, 2000
"... In this paper, I distinguish different kinds of pluralism about logical consequence. In particular, I distinguish the pluralism about logic arising from Carnap's Principle of Tolerance from a pluralism which maintains that there are different, equally "good" logical consequence relati ..."
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Cited by 1 (0 self)
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In this paper, I distinguish different kinds of pluralism about logical consequence. In particular, I distinguish the pluralism about logic arising from Carnap's Principle of Tolerance from a pluralism which maintains that there are different, equally "good" logical consequence relations on the one language. I will argue that this second form of pluralism does more justice to the contemporary state of logical theory and practice than does Carnap's more moderate pluralism.
Modelling Truthmaking
, 1999
"... Draft Only: Please do not cite According to one tradition in realist philosophy, ‘truthmaking ’ amounts to necessitation. That is, an object x is a truthmaker for the claim A if x exists, and the existence of x necessitates the truth of A. In symbols: E!x ∧ (E!x ⇒ A). I argued in my paper “Truthmake ..."
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Draft Only: Please do not cite According to one tradition in realist philosophy, ‘truthmaking ’ amounts to necessitation. That is, an object x is a truthmaker for the claim A if x exists, and the existence of x necessitates the truth of A. In symbols: E!x ∧ (E!x ⇒ A). I argued in my paper “Truthmakers, Entailment and Necessity ” [14], that if we wish to use this account of truthmaking, we ought understand the entailment connective “⇒ ” insuchaclaimasarelevant entailment, in the tradition of Anderson and Belnap and their coworkers [1, 2, 8, 11]. Furthermore, I proposed a number of theses about truthmaking as necessitation. The most controversial of these is the disjunction thesis: x makes a disjunction A ∨ B true if and only if it makes one of the disjuncts (A or B) true. That paper left one important task unfinished. I did not explain how the theses about truthmaking could be true together. In this paper I give a consistency proof, by providing a model for the theses of truthmaking in my earlier paper. This result does two things. Firstly, it shows that the theses of truthmaking
Technical Report TRARP295
 National University
, 1995
"... In this paper we consider the implications for belief revision of weakening the logic under which belief sets are taken to be closed. A widely held view is that the usual belief revision functions are highly classical, especially in being driven by consistency. We show that, on the contrary, the ..."
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In this paper we consider the implications for belief revision of weakening the logic under which belief sets are taken to be closed. A widely held view is that the usual belief revision functions are highly classical, especially in being driven by consistency. We show that, on the contrary, the standard representation theorems still hold for paraconsistent belief revision. Then we give conditions under which consistency is preserved by revisions, and we show that this modelling allows for the gradual revision of inconsistency. 1 Realistic Logics Belief Revision is a rich and diverse field. The unit of study is most often a belief set  a set K of sentences (propositions, whatever) closed under a consequence relation. In Gardenfors' canonical text [6], and in nearly all other studies of belief revision, the notion of consequence is taken to be superclassical. Consequence at least includes classical propositional consequence. This is a theoretical simplification. Noone believ...