Measuring inconsistency in generalized propositional logic. (English) Zbl 1476.03034
The notion of “measuring inconsistency” was introduced in the author’s work [Notre Dame J. Formal Logic 19, 435–444 (1978; Zbl 0305.02040)]. But the topic took off with the proposal and results in [K. Knight, J. Philos. Log. 31, No. 1, 77–98 (2002; Zbl 1003.03022)].
Let CL be classical propositional logic. As the author remarks, most of the work done on the subject has been devoted to measuring inconsistency of sets of CL-formulas.
Let GPL (generalized propositional logic) be the result of expanding CL with propositional operators similar to those characteristic of modal logic, such as, e.g., tense and spatial operators. “The goal of this paper is to find intuitively good ways to measure inconsistency as operators are added to propositional logic [CL] in the framework of generalized propositional logic” (p. 338).
In the final section of the paper, the author remarks the ensuing two facts: (1) a weak concept of inconsistency is relevant in the case of GPL, and it has been shown in the paper how to measure it; (2) it is indicated how to measure the relative inconsistency of a set of formulas. Finally, the author suggests some ideas for future work on the topic.
Let CL be classical propositional logic. As the author remarks, most of the work done on the subject has been devoted to measuring inconsistency of sets of CL-formulas.
Let GPL (generalized propositional logic) be the result of expanding CL with propositional operators similar to those characteristic of modal logic, such as, e.g., tense and spatial operators. “The goal of this paper is to find intuitively good ways to measure inconsistency as operators are added to propositional logic [CL] in the framework of generalized propositional logic” (p. 338).
In the final section of the paper, the author remarks the ensuing two facts: (1) a weak concept of inconsistency is relevant in the case of GPL, and it has been shown in the paper how to measure it; (2) it is indicated how to measure the relative inconsistency of a set of formulas. Finally, the author suggests some ideas for future work on the topic.
Reviewer: Gemma Robles (León)
References:
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