1996
DOI: 10.4324/9780203290644
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A New Introduction to Modal Logic

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Cited by 811 publications
(481 citation statements)
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“…The well-known modal logic S5 (see an introduction in [HC68]) shares with E the same set of models but the modal operators in S5 are denoted by 2 and 3. In the sequel, we write for 2 (φ 0 ) to denote the set of formulas for S5.…”
Section: Expressivity Of E With Respect To S5mentioning
confidence: 99%
“…The well-known modal logic S5 (see an introduction in [HC68]) shares with E the same set of models but the modal operators in S5 are denoted by 2 and 3. In the sequel, we write for 2 (φ 0 ) to denote the set of formulas for S5.…”
Section: Expressivity Of E With Respect To S5mentioning
confidence: 99%
“…Besides, we shall be all the more certain that X takes its value in some subset A as all the values outside A have a smaller degree of possibility; this can be estimated by means of a dual measure of necessity N(A) =1 -Π(A c ) (A c is the complement of A). This duality between possibility and necessity measures (Dubois and Prade, 1980) is a graded version of the one existing in modal logic (Hughes and Cresswell, 1968), which expresses a relation between the necessary and the possible, already advocated by Aristotle and his school; indeed some linkage between possibility theory and some modal logic systems have been pointed out (e.g., Fariñas del Cerro and Herzig, 1991). Necessity degrees N(A) express how certain the proposition "X is A" is, in the face of the possibility distribution induced by F. More precisely it expresses to what extent "X is A" is implied by "X is F", namely N(A) = I S (F, A), using (1.13) with a Kleene-Dienes implication.…”
Section: When a Is An Ordinary Subset π(A) Is Defined As The Maximummentioning
confidence: 99%
“…However, in propositional logic, uncertainty is three-valued: one can be sure about a proposition, sure about its negation, or unsure about both. Explicitly expressing and reasoning about these three situations requires the setting of modal logic (Hughes and Cresswell, 1968), where certainty is captured by the modal necessity and reflects provability, while the lack of certainty is captured by the modal possibility, and reflects logical consistency.…”
Section: World and Wordsmentioning
confidence: 99%
“…Completeness of K can be proved by e.g. the Lemmon-Scott extension of Henkin's technique of canonical models [29], [50]. Decidability of K follows from completeness and the collapse property mentioned above along with decidability of propositional calculus.…”
Section: Modal Logicmentioning
confidence: 99%
“…The derivation rules of modal propositional logic are: modus ponens M P and the necessity rule N which is the relation on formulas consisting of pairs of the form (α, [α]). This calculus is consistent [50]: to see it it suffices to collapse formulas of K onto formulas of propositional calculus by omitting all modal operator symbols. Then theorems of modal logic are in one-to-one correspondence with theorems of propositional calculus.…”
Section: Modal Logicmentioning
confidence: 99%