Formal semantics
Which "all dogs are not black" which "the dog which there is is black" which "all dogs are black" if the formal semantics (formal semantics) is the "meaning", e.g., a natural language in the semantics (program semantics) of a natural language and the computer programming language is symmetric in each sentence of "the dog which there is is not black" each; had a meaning, but was going to express (say "effects") formally as a result of having let a computer carry out the program that was going to express it or was written in formal (formal) in it in the programming language in it, how a computer worked. I mainly describe the thing of the field near natural language and it by this article. Refer to an article of the program semantics about the semantics of the programming language.
In the natural language, I regard a natural language as a kind of formal system and am a situation thinking that the meaning of the sentence is decided according to a constant procedure constitutively by the component. I aim for applying a concept to use in a meeting, mathematics including the functional symbol to a theory, and describing logical relations such as the rule of the truth condition of the sentence of the natural language or a premise, a connotation, the contradiction. It is started from a study of logician Montague, and a variety of theoretical frameworks are suggested now. It is applied to natural language processing.
Because I assume a language and direct ties with the outside world, and the formal semantics really abstracts the human cognitive activity using the language, there is the strong criticism from a researcher of the cognitive semantics mainly. But it is already noticed by the researcher of the formal semantics in the criticism, and there is the thing that theoretical improvement is tried.
Table of contents
Main concept of the formal semantics
Truth condition
I applied semantics of the abstract language employing precise grammatical constructions that アルフレト Tal was fond of the Donald David loss and stopped by to the semantics of the natural language and did the meaning of the sentence when the sentence was the condition that it was truly (truth condition). This condition is expressed by following "T-sentence (T-sentence)".
- "Snow is white," but is best as for being the truth at time when snow is white
In addition, "structure (Structure)" of the model theory is used for "translation (Interpretation)" giving a meaning in expression in the semantics of the abstract language employing precise grammatical constructions, but applies this to the semantics of the natural language in the formal semantics. For example, the name is translated as representation to an individual, and the sentence is translated as representation to a truth-value. Such a semantics is called model-theoretic semantics (Model theoritic semantics).
Furthermore, this thought is expanded in possible worlds semantics to handle the expression such as possibility and inevitability, the condition sentence. It deals with how a sentence is represented in the possible worlds semantics by the possible worlds. For example, at least one white possible world exists, and snow thinks that I am represented there in the possible worlds where snow does various colors as for the proposition that the sentence, "snow may be white" expresses.
Compositionality principle
The compositionality principle says all Fregean principle of them, and the meaning of the compound expression is a theoretical supposition that it is decided according to a constant synthetic procedure uniquely by the component (a natural language really has the expression that is not constitutive like an idiom). Montague guaranteed this principle by giving associate same model representation between the syntactic indication and semantic representation of the sentence.
For example, in the sentence John walks., the meaning rule corresponding to syntactic rules to relate walks to John is assumed. I assume instructions object of John an individual and do the instructions object of walk if it walks for an individual when it is the truth, the characteristic function which returns a false if I do not walk (this is equivalent with a set of the whole walking thing). It can prescribe the meaning rule to decide instructions object of the whole sentence then as the thing which applied function walk for John (the rule used in Montague and a subsequent study is really more complicated than this). It is common that the notation of the function uses a lambda calculation.
Difference in form (individual, function, truth-value) for instructions decided every categories such as a noun, a verb, the sentence says a type and names a theory based on the thought of the type a type theory.
Possible worlds
Birth and development of the formal semantics
The formal semantics assumes logic of syllogism and Frege of Aristotle the next source. However, an impression not to be suitable for the discussion that the natural language was vague as for these classic frames, and was close became one of the motives and did not examine the possibility to consider a natural language to be a just formal system, and to describe a meaning enough. In the early 1970s, logician Richard Montague showed the possibility that I could describe the meaning of the natural language formally and brought a big change for the meaning study of the natural language.
The frame which Montague showed is just rarely used, and a study based on some theories that developed this is active now. Particularly, the study that took a problem of a phenomenon and the context to be seen in the unit that is bigger than the sentence that Montague did not treat into account develops. I give below a main theory.
- Generalized quantifier theory
- I expand the concept of the quantification child such as) and ∃( existing) of ∀( option used in classical theory science and aim at describing the meaning of the natural language by generally arresting noun phrase expression with a quantification child. I stop at Cooper with bar Wise.
- Situation semantics
- It is the theory that I laid mainly on a language depending on the context and describes the problem of the meaning as relations with the situation that I can use verbalization and the expression for. It depends on bar Wise and Perry.
- Dynamic semantics
- It is a viewpoint to think to update a state of the knowledge because language information is combined with background information. It depends on Haym, accompaniment.
- Discourse representation theory
- I give middle indication of the statement structure and am suitable though I handle the correspondence of the pronoun beyond the sentence by the theory that the contents are transferred to whenever a sentence is input. I have a near relation with the mental space theory told to belong to cognitive linguistics. It depends on accompaniment.
Allied item
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