- Formal semantics
:"See also

."Formal semantics of programming languages **Formal semantics**is the study of thesemantics , orinterpretation s, offormal language s. A formal language can be defined apart from any interpretation of it. This is done by designating aset ofsymbol s (also called analphabet ) and a set offormation rules (also called a "formal grammar") which determine which strings of symbols arewell-formed formula s. Whentransformation rules (also called "rules of inference") are added, and certain sentences are accepted asaxiom s (together called adeductive system or a "deductive apparatus") alogical system is formed. An interpretation is an assignment ofmeaning s to these symbols andtruth-value s to its sentences. [*The Cambridge Dictionary of Philosophy, "Formal semantics"*]The truth conditions of various sentences we may encounter in

argument s will depend upon their meaning, and so conscientious 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 theproposition , an idealised sentence suitable for logical manipulation.Until the advent of modern logic,

Aristotle 's "Organon ", especially "De Interpretatione ", provided the basis for understanding the significance of logic. The introduction ofquantification , needed to solve theproblem of multiple generality , rendered impossible the kind of subject-predicate analysis that governed Aristotle's account, although there is a renewed interest interm 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:

*is the archetype ofModel-theoretic semantics Alfred Tarski 'ssemantic theory of truth , based on hisT-schema , and is one of the founding concepts ofmodel theory . This is the most widespread approach, and is based on the idea that the meaning of the various parts of the propositions are given by the possible ways we can give a recursively specified group of interpretation functions from them to some predefined mathematical domains: an interpretation offirst-order predicate logic is given by a mapping from terms to a universe ofindividual s, and a mapping from propositions to the truth values "true" and "false". Model-theoretic semantics provides the foundations for an approach to the theory of meaning known asTruth-conditional semantics , which was pioneered by Donald Davidson.Kripke semantics introduces innovations, but is broadly in the Tarskian mold.*

associates the meaning of propositions with the roles that they can play in inferences.Proof-theoretic semantics Gerhard Gentzen ,Dag Prawitz andMichael Dummett are generally seen as the founders of this approach; it is heavily influenced byLudwig Wittgenstein 's later philosophy, especially his aphorism "meaning is use".*

(also commonly referred to as "substitutional quantification") was advocated byTruth-value semantics Ruth Barcan Marcus for modal logics in the early 1960s and later championed by Dunn, Belnap, and Leblanc for standard first-order logic. James Garson has given some results in the areas of adequacy for intensional logics outfitted with such a semantics. The truth conditions for quantified formulas are given purely in terms of truth with no appeal to domains whatsoever (and hence its name "truth-value semantics").*

**Game-theoretical semantics**has made a resurgence lately mainly due toJaakko Hintikka for logics of (finite) partially ordered quantification which were originally investigated byLeon Henkin , who studied "Henkin quantifiers".*

originated from H. Field and has been shown equivalent to and a natural generalization of truth-value semantics. Like truth-value semantics, it is also non-referential in nature.Probabilistic semantics **References**

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2010.*

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**formal semantics**— noun The study of the semantics, or interpretations, of formal languages … Wiktionary**formal semantics**— noun the branch of semantics that studies the logical aspects of meaning • Hypernyms: ↑semantics … Useful english dictionary**Formal semantics of programming languages**— In theoretical computer science, formal semantics is the field concerned with the rigorous mathematical study of the meaning of programming languages and models of computation. The formal semantics of a language is given by a mathematical model… … Wikipedia**Semantics**— is the study of meaning in communication. The word derives from Greek σημαντικός ( semantikos ), significant , [cite web|url=http://www.perseus.tufts.edu/cgi bin/ptext?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3D%2393797|title=Semantikos, Henry… … Wikipedia**Formal epistemology**— is a subdiscipline of epistemology that utilizes formal methods from logic, probability theory and computability theory to elucidate traditional epistemic problems. TopicsSome of the topics that come under the heading of formal epistemology… … Wikipedia**Formal interpretation**— A formal interpretation [http://books.google.com/books?id=weKqT3ka5g0C pg=PA74 lpg=PA74 dq=%22Formal+interpretation%22+%22formal+language%22 source=web ots=pLN ms7Wi2 sig=P JqwdzOqLcX4nMpP64qmacnkDU hl=en#PPA74,M1 Cann Ronnie, Formal Semantics:… … Wikipedia**Formal proof**— See also: mathematical proof, proof theory, and axiomatic system A formal proof or derivation is a finite sequence of sentences (called well formed formulas in the case of a formal language) each of which is an axiom or follows from the… … Wikipedia**Formal grammar**— In formal semantics, computer science and linguistics, a formal grammar (also called formation rules) is a precise description of a formal language ndash; that is, of a set of strings over some alphabet. In other words, a grammar describes which… … Wikipedia**Formal verification**— In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of intended algorithms underlying a system with respect to a certain formal specification or property, using formal methods… … Wikipedia**Formal system**— In formal logic, a formal system (also called a logical system,Audi, Robert (Editor). The Cambridge Dictionary of Philosophy . Second edition, Cambridge University Press, 1999. ISBN 978 0521631365 (hardcover) and ISBN 978 0521637220 (paperback).] … Wikipedia