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G.E. Hughes & M.J. Cresswell, A New Introduction to Modal Logic, London and New York: Routledge, 1996, pp. 24-33. (2) The System K ① The system K is one which will turn out to have as its theorems precisely those modal formulae which are K-valid. ② The axioms of the system K consist of (a) all valid wff of PC (b) the single distinctively modal wff, K PC: If α is a valid wff of PC, then α is an a..

G.E. Hughes & M.J. Cresswell, A New Introduction to Modal Logic, London and New York: Routledge, 1996, pp. 23-24. (1) Systems of Modal Logic ① The axiomatic method: it allows us to define a class of wff without any reference to their meanings. ② An axiomatic basis for a logical system (a) a specification of the language in which the formulae of the system will be expressed - i.e. a list of primi..

G.E. Hughes & M.J. Cresswell, A New Introduction to Modal Logic, London and New York: Routledge, 1996, pp. 13-21. (9) Basic modal notions ① In modal logic, there are a number of non-truth-functional concepts. ② Modal Operator L (□) L: necessity operator "necessarily," "must be," "is bound to" Instead of writing "A is bound to be B," we can write "It is bound to be the case that A is B." Lp= Nece..

G.E. Hughes & M.J. Cresswell, A New Introduction to Modal Logic, London and New York: Routledge, 1996, pp. 3-13. (1) The Language of PC (Propositional Carculus) ① Primitive (or undefined) symbols of PC 1. A set of letters: p, q, r, . . . (with or without numerical subscripts). We suppose ourselves to have an unlimited number of these. 2. The following four symbols: ~, V, (, ). ※ Any symbol in th..