See: Formal System, Scientific Theory, Mathematical Theorem.
- a well-substantiated explanation of some aspect of the natural world; an organized system of accepted knowledge that applies in a variety of ...
- hypothesis: a tentative insight into the natural world; a concept that is not yet verified but that if true would explain certain facts or phenomena; "a scientific hypothesis that survives experimental testing becomes a scientific theory"; "he proposed a fresh theory of alkalis that later was ...
- a belief that can guide behavior; "the architect has a theory that more is less"; "they killed him on the theory that dead men tell no tales"
- (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Theory
- The word theory has many distinct meanings in different fields of knowledge, depending on their methodologies and the context of discussion. Definitively speaking, a theory is the analysis of a set of facts in their relation to one another.  Additionally, in contrast with a theorem the statement of the theory is generally accepted only in some tentative fashion as opposed to regarding it as having been conclusively established. This may merely indicate, as it does in the sciences, that the theory was arrived at using potentially faulty inferences (scientific induction) as opposed to the necessary inferences used in mathematical proofs. In these cases the term theory does not suggest a low confidence in the claim and many uses of the term in the sciences require just the opposite.
- (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Theory_(mathematical_logic)
- In mathematical logic, a theory is a set of sentences in a formal language. E.g. a first-order theory is a set of first-order sentences. Many authors require that the theory be closed under logical consequence.