Sentence examples for logical language from inspiring English sources

A logic is exogenous if programs are explicit in the logical language, while for endogenous logics this is not the case.

The logical language of propositional provability logic contains, in addition to propositional atoms and the usual truth-functional operators as well as the contradiction symbol ⊥, a modal operator □ with intended meaning "is provable in T," where T is a sufficiently strong formal theory, let us say Peano Arithmetic (see Section 4).

According to Quine, the propositions of a scientific theory should first be expressed in terms of predicate logic, or the predicate calculus, a logical language consisting of names, variables (which may be substituted for names), predicates (or properties), logical connectives (such as and, or, and if…then), and quantifiers.

Church's type theory is a formal logical language which includes first-order logic, but is more expressive in a practical sense.

In proposing our approach, we acknowledge the interesting previous efforts to develop a logical language for biology, based on classical logic [18], [19], [20].

This leads to the idea of adding a temporal dimension to a logic designed to reason about such models, that is to enrich the logical language with temporal operators suitable for reasoning about the evolution of the models over time.

This is especially true for the notions of set and collection in general, for the basic syntactical and semantical concepts of standard classical logic (logical languages of a given order, the notion of satisfiability, definability).

On this conception, "[l]ogic studies the truth conditions that hinge solely on grammatical constructions" (Quine 1980, 17).[4] This criterion yields appropriate results when applied to the language of first-order logic (FOL) and other standard logical languages.

Again, it is important to remember that Peirce's Existential Graphs are not just an expansion of logical languages but also underline Peirce's new approach to logic and formalization.

The most common method since the 20th century, the logical or linguistic method, relied upon theories of meaning or reference as applied to either artificial logical languages or to natural languages to dictate the kinds of entity that exist.

In logical languages, quantifier expressions are variable-binding operators.