Formal semantics

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Formal semantics may refer to:

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Formal language Words whose letters are taken from an alphabet and are well-formed according to a specific set of rules

In mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules.

The following outline is provided as an overview of and topical guide to linguistics:

Semantics is the study of meaning, reference, or truth. The term can be used to refer to subfields of several distinct disciplines including linguistics, philosophy, and computer science.

Pragmatics is a subfield of linguistics and semiotics that studies how context contributes to meaning. Pragmatics encompasses speech act theory, conversational implicature, talk in interaction and other approaches to language behavior in philosophy, sociology, linguistics and anthropology. Unlike semantics, which examines meaning that is conventional or "coded" in a given language, pragmatics studies how the transmission of meaning depends not only on structural and linguistic knowledge of the speaker and listener but also on the context of the utterance, any pre-existing knowledge about those involved, the inferred intent of the speaker, and other factors. In that respect, pragmatics explains how language users are able to overcome apparent ambiguity since meaning relies on the manner, place, time, etc. of an utterance.

Discourse

The term discourse identifies and describes written and spoken communications. In semantics and discourse analysis, a discourse is a conceptual generalization of conversation. In a field of enquiry and social practice, the discourse is the vocabulary for investigation of the subject, e.g. legal discourse, medical discourse, religious discourse, et cetera. In the works of the philosopher Michel Foucault, a discourse is “an entity of sequences, of signs, in that they are enouncements (énoncés).”

In computer science, denotational semantics is an approach of formalizing the meanings of programming languages by constructing mathematical objects that describe the meanings of expressions from the languages. Other approaches providing formal semantics of programming languages including axiomatic semantics and operational semantics.

In computer science, specifically software engineering and hardware engineering, formal methods are a particular kind of mathematically rigorous techniques for the specification, development and verification of software and hardware systems. The use of formal methods for software and hardware design is motivated by the expectation that, as in other engineering disciplines, performing appropriate mathematical analysis can contribute to the reliability and robustness of a design.

Operational semantics is a category of formal programming language semantics in which certain desired properties of a program, such as correctness, safety or security, are verified by constructing proofs from logical statements about its execution and procedures, rather than by attaching mathematical meanings to its terms. Operational semantics are classified in two categories: structural operational semantics formally describe how the individual steps of a computation take place in a computer-based system; by opposition natural semantics describe how the overall results of the executions are obtained. Other approaches to providing a formal semantics of programming languages include axiomatic semantics and denotational semantics.

Metalogic is the study of the metatheory of logic. Whereas logic studies how logical systems can be used to construct valid and sound arguments, metalogic studies the properties of logical systems. Logic concerns the truths that may be derived using a logical system; metalogic concerns the truths that may be derived about the languages and systems that are used to express truths.

In programming language theory, semantics is the field concerned with the rigorous mathematical study of the meaning of programming languages. It does so by evaluating the meaning of syntactically valid strings defined by a specific programming language, showing the computation involved. In such a case that the evaluation would be of syntactically invalid strings, the result would be non-computation. Semantics describes the processes a computer follows when executing a program in that specific language. This can be shown by describing the relationship between the input and output of a program, or an explanation of how the program will be executed on a certain platform, hence creating a model of computation.

Syntax (logic) Rules used for constructing, or transforming the symbols and words of a language

In logic, syntax is anything having to do with formal languages or formal systems without regard to any interpretation or meaning given to them. Syntax is concerned with the rules used for constructing, or transforming the symbols and words of a language, as contrasted with the semantics of a language which is concerned with its meaning.

Montague grammar is an approach to natural language semantics, named after American logician Richard Montague. The Montague grammar is based on mathematical logic, especially higher-order predicate logic and lambda calculus, and makes use of the notions of intensional logic, via Kripke models. Montague pioneered this approach in the 1960s and early 1970s.

In logic, the semantics of logic or formal semantics is the study of the semantics, or interpretations, of formal and natural languages usually trying to capture the pre-theoretic notion of entailment.

Truth-conditional semantics is an approach to semantics of natural language that sees meaning as being the same as, or reducible to, their truth conditions. This approach to semantics is principally associated with Donald Davidson, and attempts to carry out for the semantics of natural language what Tarski's semantic theory of truth achieves for the semantics of logic.

In logic and mathematics, a formal proof or derivation is a finite sequence of sentences, each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence by a rule of inference. It differs from a natural language argument in that it is rigorous, unambiguous and mechanically checkable. If the set of assumptions is empty, then the last sentence in a formal proof is called a theorem of the formal system. The notion of theorem is not in general effective, therefore there may be no method by which we can always find a proof of a given sentence or determine that none exists. The concepts of Fitch-style proof, sequent calculus and natural deduction are generalizations of the concept of proof.

Computational semantics is the study of how to automate the process of constructing and reasoning with meaning representations of natural language expressions. It consequently plays an important role in natural language processing and computational linguistics.

Interpretation may refer to:

Donkey sentences are sentences that contain a pronoun with clear meaning but whose syntactical role in the sentence poses challenges to grammarians. Such sentences defy straightforward attempts to generate their formal language equivalents. The difficulty is with understanding how English speakers parse such sentences.

Formal semantics is the study of grammatical meaning in natural languages using formal tools from logic and theoretical computer science. It is an interdisciplinary field, sometimes regarded as a subfield of both linguistics and philosophy. It provides accounts of what linguistic expressions mean and how their meanings are derived from the meanings of their parts.

Semantics is the linguistic and philosophical study of meaning in language.