Sentence examples for modal logic is from inspiring English sources

In "Modalities and Quantification" (1946) and in Meaning and Necessity (1947), Carnap interprets the object language operator of necessity as expressing at the object level the semantic notion of logical truth: "[T]he guiding idea in our constructions of systems of modal logic is this: a proposition p is logically necessary if and only if a sentence expressing p is logically true.

The most straightforward way of constructing a modal logic is to add to some standard nonmodal logical system a new primitive operator intended to represent one of the modalities, to define other modal operators in terms of it, and to add axioms or transformation rules involving those modal operators.

In the strict sense however, the term "modal logic" is reserved for the logic of the alethic modalities.

Modal logic is a rich and complex subject matter.

A final complication in the semantics for quantified modal logic is worth mentioning.

Kripke semantics for propositional modal logic is, by now, a very familiar thing.

The strict implicational fragments of the logical systems S4 and S5 of modal logic are known as C4 and C5, respectively, and their Hilbert-style axiomatizations presuppose condensed detachment as their sole rule of inference.

Some characteristic axioms of modal logic are: Lp ⊃ p and L(p ⊃ q) ⊃ (Lp ⊃ Lq).

A groundbreaking paper from this period, "A Completeness Theorem for Modal Logic," was published in the Journal of Symbolic Logic in 1959, during Kripke's freshman year at Harvard University.

Buridan's modal logic was dominant in late medieval times.

In Section 3.2 a first order modal logic was sketched, in which quantification was over objects.