Logic

New Waves in Philosophical Logic by Greg Restall

By Greg Restall

Philosophical common sense has been, and remains to be, a driver in the back of a lot development and improvement in philosophy extra generally. This assortment through up-and-coming philosophical logicians bargains with a huge variety of themes, together with, for instance, proof-theory, likelihood, context-sensitivity, dialetheism and dynamic semantics.

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To allow for such mixed interpretations, it proves useful to redefine so that it links a formula to a world w and a set V of interpretation functions. V contains all “disambiguations” of the language relative to w. The clause for the colon becomes S, V, w a: A iff S, V , V (a) A, where V is an arbitrary member of V and V is the set of V (a)-images of members of V at w. A sentence A is true in a model S, V iff S, {V }, @ A, where @ is the centre of S. So a: A is true in a model iff A is true relative to the a world and the set of interpretation functions that are a-images of the original interpretation function V .

Here, the labelled sequent xRy, x : A, x : B ⇒ y : A∧B corresponds to the two display sequents •( A ◦ B) ⇒ A ∧ B A ◦ B ⇒ •(A ∧ B) 48 Francesca Poggiolesi and Greg Restall and there is no need for an inference step to move between two sequents as they are collapsed into the one sequent. The axioms, the structural rules of weakening, contraction and cut, the logical rules ¬L, ¬R, ∧L and ∧R, the modal rules L and R form the Labelled Sequent system for the basic normal modal logic K.

1997). Impossible worlds: a modest approach. Notre Dame Journal of Formal Logic 38(4), 535–572. Quine, W. V. O. (1956). Quantifiers and propositional attitudes. Journal of Philosophy 53, 177–187. Renardel de Lavalette, G. R. (2001). A logic of modification and creation. In C. Condoravdi and G. R. R. de Lavalette (Eds), Logical Perspectives on Language and Information, pp. 197 – 219. Stanford: CSLI. Segerberg, K. (1991). The basic dynamic doxastic logic of AGM. In The Goldblatt Variations, Volume 1, pp.

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