Logic Sentence

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A logic sentence is a formal sentence that abides by a logic language.



References

2009

  • (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Sentence_(mathematical_logic)
    • In mathematical logic, a sentence of a predicate logic is a well formed formula with no free variables. A sentence is viewed by some as expressing a proposition. It makes an assertion, potentially concerning any structure of L. This assertion has a fixed truth value with respect to the structure. In contrast, the truth value of a formula (with free variables) may be indeterminate with respect to any structure. As the free variables of a formula can range over several values (which could be members of a universe, relations or functions), its truth value may vary.
  • (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Well-formed_formula
    • In computer science and mathematical logic, a well-formed formula or simply formula[1] (often abbreviated WFF, pronounced "wiff" or "wuff") is a symbol or string of symbols that is generated by the formal grammar of a formal language. To say that a string \ S is a WFF with respect to a given formal grammar \ G is equivalent to saying that \ S belongs to the language generated by \ G. A formal language can be identified with the set of its WFFs.
    • A key use of WFFs is in propositional logic and predicate logics such as first-order logic. In those contexts, a formula is a string of symbols φ for which it makes sense to ask "is φ true?", once any free variables in φ have been instantiated.
    • In formal logic, proofs can be represented by sequences of WFFs with certain properties, and the final WFF in the sequence is what is proven. This final WFF is called a theorem when it plays a significant role in the theory being developed, or a lemma when it plays an accessory role in the proof of a theorem.
  • http://en.wiktionary.org/wiki/well-formed_formula
    • A statement that is expressed in a valid, syntactically correct, manner
  • http://www.coli.uni-saarland.de/projects/milca/courses/comsem/xhtml/d0e1-gloss.xhtml
    • FOL: formulae that are built from a vocabulary, the logical symbols of FOL and first-order variables according to the syntax rules of FOL.
  • http://www.earlham.edu/~peters/courses/logsys/glossary.htm
    • Wff. Acronym of "well-formed formula", pronounced whiff. A string of symbols from the alphabet of the formal language that conforms to the grammar of the formal language. See decidable wff, formal language.
  • http://www.earlham.edu/~peters/courses/logsys/glossary.htm
    • Closed wff. In predicate logic, a wff with no free occurrences of any variable; either it has constants in place of variables, or its variables are bound, or both. Also called a sentence. See bound variables; free variables; closure of a wff.
  • http://www.earlham.edu/~peters/courses/logsys/glossary.htm
    • Open wff. In predicate logic, a wff with at least one free occurrence a variable. See free variables; propositional function. Some logicians use the terms, 1-wff, 2-wff,...n-wff for open wffs with 1 free variable, 2 free variables, ...n free variables. (Others call these 1-formula, 2-formula,...n-formula.)
  • CYC Glossary http://www.cyc.com/cycdoc/ref/glossary.html
    • well-formed formula: A formula in CycL is well-formed if it conforms to the syntax of CycL and passes all the restrictions on arity and argument types of the relations that are used in it.
  • docs.rinet.ru/KofeynyyPrimer/ch38.htm
    • expression: Results in a value of true or false.