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What (who) is modal logics - definition
TYPE OF LOGIC
Substructural logics; Substructural Logics
modal logic
FORMAL LOGIC ABLE TO EXPRESS CONCEPTS SUCH AS NECESSITY, POSSIBILITY, PROVABILITY, OBLIGATION, KNOWLEDGE ETC.
Contingent truth; Modal Logic; Metaphysical contingency; Necessary propositions; Impossible propositions; Actual propositions; Semantics of modal logic; Modal logic S5; Necessity (modal logic); Necessity (logic); Necessary (modal logic); Necessary (logic); Intensional logics; Rule of necessitation; Alethic modal logic; Alethic logic; System K; ⟠; Impossible proposition; Metaphysics of modalities; Modalized; Necessary proposition; 4 (axiom); 5 (axiom); History of modal logic; Axioms of modal logic; Semantics for modal logic
<logic> An extension of propositional calculus with
operators that express various "modes" of truth. Examples
of modes are: necessarily A, possibly A, probably A, it has
always been true that A, it is permissible that A, it is
believed that A.
"It is necessarily true that A" means that things being as
they are, A must be true, e.g.
"It is necessarily true that x=x" is TRUE
while
"It is necessarily true that x=y" is FALSE
even though "x=y" might be TRUE.
Adding modal operators [F ] and [P ], meaning, respectively,
henceforth and hitherto leads to a "temporal logic".
Flavours of modal logics include: {Propositional Dynamic
Logic} (PDL), Propositional Linear Temporal Logic (PLTL),
Linear Temporal Logic (LTL), Computational Tree Logic
(CTL), Hennessy-Milner Logic, S1-S5, T.
C.I. Lewis, "A Survey of Symbolic Logic", 1918, initiated the
modern analysis of modality. He developed the logical systems
S1-S5. JCC McKinsey used algebraic methods ({Boolean
algebras} with operators) to prove the decidability of Lewis'
S2 and S4 in 1941. Saul Kripke developed the {relational
semantics} for modal logics (1959, 1963). Vaughan Pratt
introduced dynamic logic in 1976. Amir Pnuelli proposed the
use of temporal logic to formalise the behaviour of
continually operating concurrent programs in 1977.
[Robert Goldblatt, "Logics of Time and Computation", CSLI
Lecture Notes No. 7, Centre for the Study of Language and
Information, Stanford University, Second Edition, 1992,
(distributed by University of Chicago Press) ].
[Robert Goldblatt, "Mathematics of Modality", CSLI Lecture
Notes No. 43, Centre for the Study of Language and
Information, Stanford University, 1993, (distributed by
University of Chicago Press) ].
[G.E. Hughes and M.J. Cresswell, "An Introduction to Modal
Logic", Methuen, 1968 ].
[E.J. Lemmon (with Dana Scott), "An Introduction to Modal
Logic", American Philosophical Quarterly Monograpph Series,
no. 11 (ed. by Krister Segerberg), Basil Blackwell, Oxford,
1977 ].
(1995-02-15)
Modal logic
FORMAL LOGIC ABLE TO EXPRESS CONCEPTS SUCH AS NECESSITY, POSSIBILITY, PROVABILITY, OBLIGATION, KNOWLEDGE ETC.
Contingent truth; Modal Logic; Metaphysical contingency; Necessary propositions; Impossible propositions; Actual propositions; Semantics of modal logic; Modal logic S5; Necessity (modal logic); Necessity (logic); Necessary (modal logic); Necessary (logic); Intensional logics; Rule of necessitation; Alethic modal logic; Alethic logic; System K; ⟠; Impossible proposition; Metaphysics of modalities; Modalized; Necessary proposition; 4 (axiom); 5 (axiom); History of modal logic; Axioms of modal logic; Semantics for modal logic
Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics.
Modal operator
LOGICAL OPERATOR IN MODAL LOGIC
Modal connective
A modal connective (or modal operator) is a logical connective for modal logic. It is an operator which forms propositions from propositions.
Wikipedia
Substructural logic
In logic, a substructural logic is a logic lacking one of the usual structural rules (e.g. of classical and intuitionistic logic), such as weakening, contraction, exchange or associativity. Two of the more significant substructural logics are relevance logic and linear logic.
