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Directory:Jon Awbrey/Papers/Propositional Equation Reasoning Systems (view source)
Revision as of 03:41, 1 October 2010
, 03:41, 1 October 2010→Axioms: fix typo
All of the axioms in this set have the form of equations. This means that all of the inference licensed by them are reversible. The proof annotation scheme employed below makes use of a double bar <math>\overline{\underline{~~~~~~}}</math> to mark this fact, but it will often be left to the reader to decide which of the two possible ways of applying the axiom is the one that is called for in a particular case.
All of the axioms in this set have the form of equations. This means that all of the inference licensed by them are reversible. The proof annotation scheme employed below makes use of a double bar <math>\overline{\underline{~~~~~~}}</math> to mark this fact, but it will often be left to the reader to decide which of the two possible ways of applying the axiom is the one that is called for in a particular case.
Peirce introduced these formal equations at a level of abstraction that is one step higher than their customary interpretations as propositional calculi, which two readings he called the ''Entitative'' and the ''Existential'' interpretations, here referred to as <math>\operatorname{En}</math> and <math>\operatorname{Ex}</math>, respectively. The early CSP, as in his essay on ”Qualitative Logic”, and also GSB, emphasized the <math>\operatorname{En}</math> interpretation, while the later CSP developed mostly the <math>\operatorname{Ex}</math> interpretation.
Peirce introduced these formal equations at a level of abstraction that is one step higher than their customary interpretations as propositional calculi, which two readings he called the ''Entitative'' and the ''Existential'' interpretations, here referred to as <math>\operatorname{En}</math> and <math>\operatorname{Ex}</math>, respectively. The early CSP, as in his essay on “Qualitative Logic”, and also GSB, emphasized the <math>\operatorname{En}</math> interpretation, while the later CSP developed mostly the <math>\operatorname{Ex}</math> interpretation.
===Frequently used theorems===
===Frequently used theorems===