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| author | dos-reis <gdr@axiomatics.org> | 2010-04-04 17:20:33 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2010-04-04 17:20:33 +0000 |
| commit | ae3725b1b6208264518fbcd4d7adadd68978d26f (patch) | |
| tree | 5d54b04001178fdfbf0eaa4a5031658e092d2aa2 /src/algebra/boolean.spad.pamphlet | |
| parent | da7d92d632deab11bb2c93a9b51dc4972707003d (diff) | |
| download | open-axiom-ae3725b1b6208264518fbcd4d7adadd68978d26f.tar.gz | |
* algebra/boolean.spad.pamphlet (BooleanLogic): New.
(PropositionalLogic): Extend it.
* algebra/aggcat.spad.pamphlet (BitAggregate): Likewise.
* algebra/si.spad.pamphlet (SingleInteger): Assert membership to
BooleanLogic.
Diffstat (limited to 'src/algebra/boolean.spad.pamphlet')
| -rw-r--r-- | src/algebra/boolean.spad.pamphlet | 35 |
1 files changed, 24 insertions, 11 deletions
diff --git a/src/algebra/boolean.spad.pamphlet b/src/algebra/boolean.spad.pamphlet index 9be8f2a3..d4a2f65d 100644 --- a/src/algebra/boolean.spad.pamphlet +++ b/src/algebra/boolean.spad.pamphlet @@ -12,7 +12,24 @@ \tableofcontents \eject -\section{category PROPLOG PropositionalLogic} +\section{Categories an domains for logic} + +<<category BOOLE BooleanLogic>>= +)abbrev category BOOLE BooleanLogic +++ Author: Gabriel Dos Reis +++ Date Created: April 04, 2010 +++ Date Last Modified: April 04, 2010 +++ Description: +++ This is the category of Boolean logic structures. +BooleanLogic(): Category == Type with + not: % -> % + ++ \spad{not x} returns the complement or negation of \spad{x}. + and: (%,%) -> % + ++ \spad{x and y} returns the conjunction of \spad{x} and \spad{y}. + or: (%,%) -> % + ++ \spad{x or y} returns the disjunction of \spad{x} and \spad{y}. +@ + <<category PROPLOG PropositionalLogic>>= )abbrev category PROPLOG PropositionalLogic ++ Author: Gabriel Dos Reis @@ -20,17 +37,11 @@ ++ Date Last Modified: May 27, 2009 ++ Description: This category declares the connectives of ++ Propositional Logic. -PropositionalLogic(): Category == SetCategory with +PropositionalLogic(): Category == Join(BooleanLogic,SetCategory) with true: % ++ true is a logical constant. false: % ++ false is a logical constant. - not: % -> % - ++ not p returns the logical negation of `p'. - and: (%, %) -> % - ++ p and q returns the logical conjunction of `p', `q'. - or: (%, %) -> % - ++ p or q returns the logical disjunction of `p', `q'. implies: (%,%) -> % ++ implies(p,q) returns the logical implication of `q' by `p'. equiv: (%,%) -> % @@ -641,11 +652,9 @@ KleeneTrivalentLogic(): Public == Private where <<*>>= <<license>> -<<domain REF Reference>> +<<category BOOLE BooleanLogic>> <<category LOGIC Logic>> <<domain BOOLEAN Boolean>> -<<domain IBITS IndexedBits>> -<<domain BITS Bits>> <<category PROPLOG PropositionalLogic>> <<domain PROPFRML PropositionalFormula>> @@ -654,6 +663,10 @@ KleeneTrivalentLogic(): Public == Private where <<domain KTVLOGIC KleeneTrivalentLogic>> +<<domain IBITS IndexedBits>> +<<domain BITS Bits>> +<<domain REF Reference>> + @ \eject \begin{thebibliography}{99} |