Search results
Results from the WOW.Com Content Network
It is also called propositional logic, [2] statement logic, [1] sentential calculus, [3] sentential logic, [1] or sometimes zeroth-order logic. [ 4 ] [ 5 ] It deals with propositions [ 1 ] (which can be true or false ) [ 6 ] and relations between propositions, [ 7 ] including the construction of arguments based on them. [ 8 ]
In propositional logic, a propositional formula is a type of syntactic formula which is well formed. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional formula may also be called a propositional expression, a sentence, or a sentential formula.
In propositional logic and Boolean algebra, De Morgan's laws, [1] [2] [3] also known as De Morgan's theorem, [4] are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan , a 19th-century British mathematician.
To make proofs explicit, we move from the proof-less judgment "A" to a judgment: "π is a proof of (A)", which is written symbolically as "π : A". Following the standard approach, proofs are specified with their own formation rules for the judgment "π proof". The simplest possible proof is the use of a labelled hypothesis; in this case the ...
This resolution technique uses proof by contradiction and is based on the fact that any sentence in propositional logic can be transformed into an equivalent sentence in conjunctive normal form. [4] The steps are as follows. All sentences in the knowledge base and the negation of the sentence to be proved (the conjecture) are conjunctively ...
Depending on the underlying logic, the problem of deciding the validity of a formula varies from trivial to impossible. For the common case of propositional logic, the problem is decidable but co-NP-complete, and hence only exponential-time algorithms are believed to exist for general proof tasks.
Proofs employ logic expressed in mathematical symbols, along with natural language which usually admits some ambiguity. In most mathematical literature, proofs are written in terms of rigorous informal logic. Purely formal proofs, written fully in symbolic language without the involvement of natural language, are considered in proof theory.
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. [1]