S. A. Kripke. Semantic analysis of modal logic. I: Normal propositional calculi. Zeitschrift f ur Mathematische Logik und Grundlagen der Mathematik, 9:67--96, 1963.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....With Sylvan (n e Routley) Meyer proposed in [19] and [18] a minimal positive relevant logic B . As they conceived it, B had a role to play for relevant logics analogous to that played by the system K among normal modal logics with a Kripke style possible worlds semantics in the style of [16]. That is, B satisfied just those semantical postulates that we took to be common to arbitrary positive logics in the relevant family. Thus on our semantics other positive logics arose from B on the addition of specific postulates. But the main ideas e.g. that B #C is true at a world w ....

S. Kripke. Semantical analysis of modal logic. I. normal modal propositional calculus. Zeitschrift f ur Mathematische Logik und Grundlagen der Mathematik, 9:67--96, 1963.

....agent is said to know if an impartial, omniscient observer would say that the agent s state carried the information . We now proceed to interpret our formal language. While it is entirely possible to do so directly with respect to VSK systems, we will nd it bene cial to use Kripke semantics [13] in order to prove completeness of an axiomatisation. In particular, we will use Kripke frames de ned by three relations on their support set. De nition 3.2 (Kripke frames and models) A frame F is a tuple F = hW; RV ; RS ; RK i, where W is a non empty set (whose elements are called worlds) and ....

S. Kripke. Semantical analysis of modal logic. Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik, 9:67-96, 1963.

....are extensions of Propositional Logic with a necessity operator 2 and a possibly operator 3. The mono modal logics satisfying the K axiom 2(p ) q) 2p ) 2q) and the necessitation rule if p then 2p are called normal modal logics [1] They admit a Kripke style possible worlds semantics [9, 10]. For many of the normal modal logics one can split an interpretation into a frame part and a valuation part. The frame part consists of a set of possible worlds and a binary relation between these worlds, the accessibility relation. The valuation part assigns subsets of the possible worlds to ....

S. A. Kripke. Semantical analysis of modal logic I, normal propositional calculi. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik, 9:67-96, 1963.

.... this in more detail in Section 5; an overview of S5 and related logics of knowledge and belief can be found in [HM2] Indeed, the abstract models most frequently used to capture this notion (for example, in [Ro] have been variants of the classical Kripke style possible worlds model for S5 [Kr]. But, a priori, it is not the least bit clear that this is the appropriate abstraction for the notion of knowledge in which we are interested. Does each state of an S5 Kripke structure really correspond to some knowledge situation that the system can be in As we shall show, the answer to 2 ....

....their knowledge. Put differently, it is what someone who had all the knowledge that each member in the group had could infer. We shall soon give the semantics that tells us when a formula is true at a point in an interpreted system. Since our semantics is based on the standard Kripke semantics [Kr], we begin by reviewing the Kripke semantics for the truth of a formula at a state of a Kripke structure (where we follow Halpern and Moses [HM2] in the definition of the truth of a formula involving distributed knowledge) A Kripke structure is a tuple 15 (S; K 1 ; K n ) where S is a set ....

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S. Kripke, Semantical analysis of modal logic, Zeitschrift f ur mathematische Logik und Grundlagen der Mathematik 9 (1963), pp. 67--96.

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S. A. Kripke. Semantic analysis of modal logic. I: Normal propositional calculi. Zeitschrift f ur Mathematische Logik und Grundlagen der Mathematik, 9:67--96, 1963.

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