Difference between revisions of "Propositional logic"
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'''Propositional logic''' is the [[logical system]] which takes [[sentence]]s and their combinations as primitives. The [[logical constant]]s of the language are negation and the connectives &, v, ->, and <->. [[Propositional letters]] (also ''atomic propositions'') are combined with these connectives into more complex [[propositional formula]]s according to the syntax of propositional logic. The semantics interprets the meaning of the logical constants in terms of [[truth-value]]s. Propositional logic characterizes a particular class of valid arguments, like the one in (i). | '''Propositional logic''' is the [[logical system]] which takes [[sentence]]s and their combinations as primitives. The [[logical constant]]s of the language are negation and the connectives &, v, ->, and <->. [[Propositional letters]] (also ''atomic propositions'') are combined with these connectives into more complex [[propositional formula]]s according to the syntax of propositional logic. The semantics interprets the meaning of the logical constants in terms of [[truth-value]]s. Propositional logic characterizes a particular class of valid arguments, like the one in (i). | ||
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Translation into propositional logic makes it clear that the argument in (i) is valid because of certain logical constants. The validity of the schema in (iii) can be demonstrated with a formal syntactic deduction or by means of a truth-table. | Translation into propositional logic makes it clear that the argument in (i) is valid because of certain logical constants. The validity of the schema in (iii) can be demonstrated with a formal syntactic deduction or by means of a truth-table. | ||
| − | + | ==Links == | |
| − | + | *[http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Propositional+logic&lemmacode=455 Utrecht Lexicon of Linguistics] | |
| − | [http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Propositional+logic&lemmacode=455 Utrecht Lexicon of Linguistics] | ||
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| + | == References == | ||
* Gamut, L.T.F. 1991. ''Logic, language, and meaning,'' Univ. of Chicago Press, Chicago. | * Gamut, L.T.F. 1991. ''Logic, language, and meaning,'' Univ. of Chicago Press, Chicago. | ||
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[[Category:Semantics]] | [[Category:Semantics]] | ||
Latest revision as of 19:16, 27 September 2014
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Definition
Propositional logic is the logical system which takes sentences and their combinations as primitives. The logical constants of the language are negation and the connectives &, v, ->, and <->. Propositional letters (also atomic propositions) are combined with these connectives into more complex propositional formulas according to the syntax of propositional logic. The semantics interprets the meaning of the logical constants in terms of truth-values. Propositional logic characterizes a particular class of valid arguments, like the one in (i).
(i) If the sun is shining, then John is happy
The sun is shining
Therefore, John is happy
When we translate the natural language statements in (i) into propositional logic (as in (ii)) we get the schema in (iii).
(ii) p: the sun is shining
q: John is happy
(iii) p -> q
p
------
q
Translation into propositional logic makes it clear that the argument in (i) is valid because of certain logical constants. The validity of the schema in (iii) can be demonstrated with a formal syntactic deduction or by means of a truth-table.
Links
References
- Gamut, L.T.F. 1991. Logic, language, and meaning, Univ. of Chicago Press, Chicago.
