Difference between revisions of "Logic and Computation"
From Wiki Notes @ WuJiewen.com, by Jiewen Wu
| Line 11: | Line 11: | ||
*Connectives; | *Connectives; | ||
*Brackets. | *Brackets. | ||
| + | |||
| + | A well-formed formula (wff) is defined inductively as follows: | ||
| + | * prime propositions including proposition letters, constants; | ||
| + | * any compound propositions for formulas p and q: ~p, p/\q, p\/q, p=>q, p<=>q. | ||
| + | Normally we assume the precedence of operators as brackets, ~, /\, \/, =>, <=>. The right associativity is assumed too, e.g., p=>(q=>r). | ||
==References== | ==References== | ||
[[Category:Logic and Reasoning]] | [[Category:Logic and Reasoning]] | ||
Revision as of 10:42, 4 August 2009
Introduction
This page is to setup to summarize fundamentals of common logics.
Every logic consists of its syntax, semantic and proof theories.
Boolean Logic
It is also known as propositional logic, where a countably infinite alphabet of boolean variables can take two values either true or false.
Syntax
- Constants: true and false;
- Propositional letters;
- Connectives;
- Brackets.
A well-formed formula (wff) is defined inductively as follows:
- prime propositions including proposition letters, constants;
- any compound propositions for formulas p and q: ~p, p/\q, p\/q, p=>q, p<=>q.
Normally we assume the precedence of operators as brackets, ~, /\, \/, =>, <=>. The right associativity is assumed too, e.g., p=>(q=>r).
