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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 138 (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
Negation In Relevant Logics (How I stopped worrying and learned to love the Routley Star)
 BULLETIN OF THE SECTION OF LOGIC
, 1999
"... Negation raises three thorny problems for anyone seeking to interpret relevant logics. The frame semantics for negation in relevant logics involves a `point shift' operator . Problem number one is the interpretation of this operator. Relevant logics commonly interpreted take the inference fr ..."
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Cited by 22 (11 self)
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Negation raises three thorny problems for anyone seeking to interpret relevant logics. The frame semantics for negation in relevant logics involves a `point shift' operator . Problem number one is the interpretation of this operator. Relevant logics commonly interpreted take the inference from A and ¸A B to B to be invalid, because the corresponding relevant conditional A (¸ A B) ! B is not a theorem. Yet we often make the inference from A and ¸A B to B, and we seem to be reasoning validly when we do so. Problem number two is explaining what is really going on here. Finally, we can add an operation which Meyer has called Boolean negation to our logic, which is evaluated in the traditional way: x j= \GammaA if and only if x 6j= A. Problem number three involves deciding which is the `real' negation. How can we decide between orthodox negation and the new, `Boolean' negation. In this paper, I present a new interpretation of the frame semantics for relevant logics which will allow u...
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 Draft Only: Please do not cite According to one tradition in realist philosophy, ‘truthmaking ’ amounts to necessitation.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
INFORMATION FLOW AND IMPOSSIBLE SITUATIONS ∗
"... Classical semantic information (CSI) assigns the same body of semantic information (Cont) as well as the same amount of semantic information (cont or inf) to logically equivalent sentences. A corollary of this fact is that all logically true sentences will receive a null assignment of semantic infor ..."
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Classical semantic information (CSI) assigns the same body of semantic information (Cont) as well as the same amount of semantic information (cont or inf) to logically equivalent sentences. A corollary of this fact is that all logically true sentences will receive a null assignment of semantic information via Cont as well as a zero measure of semantic information via cont or inf. The originators of CSI allowed that there be (but did not develop) a sensible notion of psychological information (PI) whereby its measure on logically true sentences would be greater than zero. By extension they allowed that this notion of PI would be such that nonidentical measures could be assigned to logically equivalent sentences in general. The task undertaken in the article is to specify the basis of a theory of PI that satisfies these constraints. This project utilizes the frame semantics of substructural logics. The threat of a perceived ad hoc association is countered by an independent argument for the explication of the incomplete and inconsistent worlds (impossible situations) constituting frame semantics in terms of confused doxastic states. Combined with existing interpretations of frame semantics in terms of information flow, the result is a specification of the basis of a novel theory of the information flow between the doxastic states of agents, i.e. the specification of the basis of a novel theory of PI. A substructural logic no stronger than the linear logic DMALL is proposed as providing the appropriate semantics. ∗ I am indebted to Luciano Floridi, Greg Restall, Antony Eagle, Joel Mason and especially Patrick Allo for saving me from myself on more than one occasion. I would also like to thank an anonymous referee at Logique et Analyse for making many insightful suggestions and for bringing several errors to my attention. Any that remain are entirely my responsibility.
Logics, Situations and Channels ∗
, 2006
"... The notion of that information is relative to a context is important in many different ways. The idea that the context is small — that is, not necessarily a consistent and complete possible world — plays a role not only in situation theory, but it is also an enlightening perspective from which to vi ..."
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The notion of that information is relative to a context is important in many different ways. The idea that the context is small — that is, not necessarily a consistent and complete possible world — plays a role not only in situation theory, but it is also an enlightening perspective from which to view other areas, such as modal logics, relevant logics, categorial grammar and much more. In this article we will consider these areas, and focus then on one further question: How can we account for information about one thing giving us information about something else? This is a question addressed by channel theory. We will look at channel theory and then see how the issues of information flow and conditionality play a role in each of the different domains we have examined. 1