. Theories, in the sense in which arithmetic is a theory, are decidable if formalizations exist for them which are COMPLETE. In systems without CONTINGENT propositions, such as formalizations of arithmetic, a well-formed formula (see AXIOM SYSTEM) is...

Decidable and Undecidable Theories Suppose T is a theory (i.e., a set of sentences) in a formal language L of logic. A decision procedure for T is a mechanical procedure for calculating whether any given sentence of L is a logical consequence of T . We...

The word decidable may refer to: Decision Decidable language Decidability (logic) for the equivalent in mathematical logic Gödel's incompleteness theorem, a theorem on the indecidability of languages consisting of "true statements" in mathematical...

When it comes to dealing with the possibility of removing Alan Hevesi, it already seems clear what direction they're going to be pushing him in. The 18-member committee Spitzer has formed to advise him on government reform includes a number of people who have already...

Price-Fixing: A Wisconsin station owner sells gasoline at a discount to senior citizens. And what does he get in return? A commendation from the city council? No, he's told that he's in violation of the law.Raj Bhandari has been allowing senior citizens a 2-cent discount...

The Supreme Court ruled Monday that local governments can compel private trash haulers to use municipal facilities, even if it would cost more to keep garbage at home than to dispose of it elsewhere.The ruling upholding local ordinances in upstate New York protects a stream...

Portugal is deciding in a national referendum Sunday whether to discard its strict abortion law, a battle that pits the Socialist government against conservative parties and the Catholic Church.The center-left Socialist government wants to grant women the right to opt for abortion during the first...