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Example of a logic model for a school-based self-management educational interventions for asthma in children and adolescents. Logic models are hypothesized descriptions of the chain of causes and effects leading from inputs and activities to an outcome of interest (e.g. prevalence of cardiovascular diseases, annual traffic collision, etc.).
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]
Fuzzy logic is based on the observation that people make decisions based on imprecise and non-numerical information. Fuzzy models or fuzzy sets are mathematical means of representing vagueness and imprecise information (hence the term fuzzy). These models have the capability of recognising, representing, manipulating, interpreting, and using ...
In logic, a set of symbols is commonly used to express logical representation. ... necessity (in a model) box; it is necessary that modal logic:
In first-order logic with equality, only normal models are considered, and so there is no term for a model other than a normal model. When first-order logic without equality is studied, it is necessary to amend the statements of results such as the Löwenheim–Skolem theorem so that only normal models are considered.
There are a few other reasons to restrict study of first-order logic to normal models. First, it is known that any first-order interpretation in which equality is interpreted by an equivalence relation and satisfies the substitution axioms for equality can be cut down to an elementarily equivalent interpretation on a subset of the original domain.
For instance, the Interior Semantics interprets formulas of modal logic as follows. A topological model is a tuple = ,, where , is a topological space and is a valuation function which maps each atomic formula to some subset of . The basic interior semantics interprets formulas of modal logic as follows:
In mathematical logic, abstract model theory is a generalization of model theory that studies the general properties of extensions of first-order logic and their models. [ 1 ] Abstract model theory provides an approach that allows us to step back and study a wide range of logics and their relationships. [ 2 ]