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In logic, formal semantics OR logical semantics,^{[1]}^{[2]}^{[3]} is the study of the semantics, or interpretations, of formal and (idealizations of) natural languages usually trying to capture the pre-theoretic notion of entailment. (Although both linguistics and logic lay claim to providing theories of natural language, according to Geach, logic generally ignores the "idiotism of idiom", and sees natural languages as cluttered with idioms of no logical interest.)^{[4]}
The truth conditions of various sentences we may encounter in arguments will depend upon their meaning, and so logicians cannot completely avoid the need to provide some treatment of the meaning of these sentences. The semantics of logic refers to the approaches that logicians have introduced to understand and determine that part of meaning in which they are interested; the logician traditionally is not interested in the sentence as uttered but in the proposition, an idealised sentence suitable for logical manipulation.
Until the advent of modern logic, De Interpretatione, provided the basis for understanding the significance of logic. The introduction of quantification, needed to solve the problem of multiple generality, rendered impossible the kind of subject-predicate analysis that governed Aristotle's account, although there is a renewed interest in term logic, attempting to find calculi in the spirit of Aristotle's syllogistic but with the generality of modern logics based on the quantifier.
The main modern approaches to semantics for formal languages are the following:
Epistemology, Computer science, Philosophy, Aesthetics, Metaphysics
Linguistics, Semantic Web, Semiotics, Logic, Language
Logic, Logical truth, Mathematical logic, Set theory, Philosophical logic
Logic, Mathematical logic, String (computer science), Semantics, Set theory
Set theory, Logic, Logical consequence, Truth, Foundations of mathematics
Computer science, Logic, Linguistics, Education, Modal logic