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A satisfiable theory is a theory that has a model. This means there is a structure M that satisfies every sentence in the theory. Any satisfiable theory is syntactically consistent, because the structure satisfying the theory will satisfy exactly one of φ and the negation of φ, for each sentence φ.
A set of sentences is called a theory; thus, individual sentences may be called theorems. To properly evaluate the truth (or falsehood) of a sentence, one must make reference to an interpretation of the theory. For first-order theories, interpretations are commonly called structures. Given a structure or interpretation, a sentence will have a ...
In a deductive theory, any sentence which is a logical consequence of one or more of the axioms is also a sentence of that theory. [11] This is called the received view of theories. In the semantic view of theories, which has largely replaced the received view, [18] [19] theories are viewed as scientific models. A model is an abstract and ...
Being a constraint on x-bar theory, the criterion aims to parse out ill-formed sentences. Thus, if the number or categories of arguments in a sentence does not meet the theta-role assigner's requirement in any given sentence, that sentence will be deemed ungrammatical. (Carnie 2007, p. 224).
Truth conditions of a sentence do not necessarily reflect current reality. They are merely the conditions under which the statement would be true. [1] More formally, a truth condition makes for the truth of a sentence in an inductive definition of truth (for details, see the semantic theory of truth).
In Dowty’s theory of thematic proto-roles, semantic roles are considered as prototype notions, in which there is a prototypical agent role that has those traits characteristically associated to it, while other thematic roles have less of those traits and are accordingly proportionally more distant to the prototypical agent. [6]
Consider a sentence such as "There's an electron in the sink." This means something along the lines of: "There exist some properties P 1 , P 2 , ..., P n ( one for every theoretical property involved in the scientific theory, with 'electronhood' (which roughly corresponds to the essence of an electron included as P 1 ) such that...
The Projection Principle simply states that when notating the syntactic structure of a sentence such as “John runs fast.”, we must specify at every level what lexical category each piece of the sentence belongs to [2] Two common ways of notating the syntactic structure of a sentence under X-Bar Theory include bracketing and tree drawing.