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I need a modal logic, where inconsistency between formulas in not binary: a pair of formulas may be more or less inconsistent. The modal operators express uncertainty. So the formulas which would be contradictory without the modal operators can have some "fuzzy" inconsistency with the modal operators. Did somebody encounter such a logic? If not, is there something wrong with such a logic?

I need a first order modal logic, where inconsistency between formulas in not binary: a pair of formulas may be more or less inconsistent. The modal operators express uncertainty. So the formulas which would be contradictory without the modal operators can have some "fuzzy" inconsistency with the modal operators. Did somebody encounter such a logic? If not, is there something wrong with such a logic?

I need a modal logic, where inconsistency between formulas in not binary: a pair of formulas may be more or less inconsistent. The modal operators express uncertainty. So the formulas which would be contradictory without the modal operators can have some "fuzzy" inconsistency with the modal operators. Did somebody encounter such a logic?

I need a modal logic, where inconsistency between formulas in not binary: a pair of formulas may be more or less inconsistent. The modal operators express uncertainty. So the formulas which would be contradictory without the modal operators can have some "fuzzy" inconsistency with the modal operators. Did somebody encounter such a logic? If not, is there something wrong with such a logic?