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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 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 ...
The intended interpretation is called the standard model (a term introduced by Abraham Robinson in 1960). [6] In the context of Peano arithmetic, it consists of the natural numbers with their ordinary arithmetical operations. All models that are isomorphic to the one just given are also called standard; these models all satisfy the Peano axioms.
Boolean-valued model; Kripke semantics. General frame; Predicate logic. First-order logic. Infinitary logic; Many-sorted logic; Higher-order logic. Lindström quantifier; Second-order logic; Soundness theorem; Gödel's completeness theorem. Original proof of Gödel's completeness theorem; Compactness theorem; Löwenheim–Skolem theorem. Skolem ...
A model with this condition is called a full model, and these are the same as models in which the range of the second-order quantifiers is the powerset of the model's first-order part. [3] Thus once the domain of the first-order variables is established, the meaning of the remaining quantifiers is fixed.
Mathematical logic is the study of formal logic within mathematics.Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory).
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.