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  5. Adding the Everywhere Operator to Propositional Logic

Adding the Everywhere Operator to Propositional Logic

File(s)
96-1583.pdf (197.89 KB)
96-1583.ps (343.55 KB)
Permanent Link(s)
https://hdl.handle.net/1813/7239
Collections
Computer Science Technical Reports
Author
Gries, David
Schneider, Fred B.
Abstract

Sound and complete modal propositional logic C is presented, in which "P" has the interpretation "P is true in all states". The interpretation is already known as the Carnapian extension of S5. A new axiomatization for C provides two insights. First, introducing an inference rule "textual substitution" allows seamless integration of the propositional and modal parts of the logic, giving a more practical system for writing formal proofs. Second, the two following approaches to axiomatizing a logic are shown to be not equivalent: (i) give axiom schemes that denote an infinite number of axioms and (ii) write a finite number of axioms in terms of propositional variables and introduce a substitution inference rule.

Date Issued
1996-05
Publisher
Cornell University
Keywords
computer science
•
technical report
Previously Published as
http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR96-1583
Type
technical report

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