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In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the statements of the theory hold). [1]
This statistical model defines a similarity metric, whereby sentences which are more like those within a corpus in certain respects are assigned higher values than sentences less alike. Pereira's model assigns an ungrammatical version of the same sentence a lower probability than the syntactically well-formed structure demonstrating that ...
List or describe a set of sentences in the language L σ, called the axioms of the theory. Give a set of σ-structures, and define a theory to be the set of sentences in L σ holding in all these models. For example, the "theory of finite fields" consists of all sentences in the language of fields that are true in all finite fields. An L σ ...
A physical model (most commonly referred to simply as a model but in this context distinguished from a conceptual model) is a smaller or larger physical representation of an object, person or system. The object being modelled may be small (e.g., an atom ) or large (e.g., the Solar System ) or life-size (e.g., a fashion model displaying clothes ...
Let ψ be a sentence in first-order logic.The spectrum of ψ is the set of natural numbers n such that there is a finite model for ψ with n elements.. If the vocabulary for ψ consists only of relational symbols, then ψ can be regarded as a sentence in existential second-order logic (ESOL) quantified over the relations, over the empty vocabulary.
For example, generative theories generally provide competence-based explanations for why English speakers would judge the sentence in (1) as odd. In these explanations, the sentence would be ungrammatical because the rules of English only generate sentences where demonstratives agree with the grammatical number of their associated noun. [14]
In any case, users of a model need to understand the assumptions made that are pertinent to its validity for a given use. Building a model requires abstraction. Assumptions are used in modelling in order to specify the domain of application of the model. For example, the special theory of relativity assumes an inertial frame of reference.
A classic example of computational modeling in language research is McClelland and Elman's TRACE model of speech perception. [13] A model of sentence processing can be found in Hale (2011)'s 'rational' Generalized Left Corner parser. [14] This model derives garden path effects as well as local coherence phenomena.