Vigan`o, L. (1997). A Framework for Non-Classical Logics. PhD thesis, Universitat des Saarlandes. Wickline, P., Lee, P., Pfenning, F., and Davies, R. (1998). Modal types as staging specifications for run-time code generation. ACM Computing Surveys, 30(3es).  Home/Search Document Not in Database Summary Related Articles Check |
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A Judgmental Reconstruction of Modal Logic - Pfenning, Davies (2001) (1 citation) (Correct)
....This concludes the treatment of validity and propositions of the form 2A. In order to discuss the computational interpretations of 2A, we reexamine the rules with a proof term assignment in Section 6. Necessity can be characterized axiomatically by the following three axioms (see, for example, [Vig97, Kob97, AdPR98]) together with the inference rule of necessitation which allows 2A true to be derived from A true. 2A oe A true The derivations of these axioms in natural deduction is given in Section 6 in abbreviated form as proof terms. We conclude this section with a remark on two of Prawitz s ....
.... proposition A is true in world w , and world w is reachable from world w . While more verbose and requiring explicit reasoning about worlds, this approach is also more flexible in that various traditional modal logics can be expressed simply by varying the reachability judgment. Vigan o [Vig97] has conducted a systematic study of modal logic via Kripke structures from the point of view of logical frameworks. In certain cases this can be simplified to obtain a formulation of natural deduction employing a stack of contexts, representing a path through the Kripke structure. Variations of ....
Luca Vigan`o. A Framework for Non-Classical Logics. PhD thesis, Universitat des Saarlandes, September 1997.
Under consideration for publication in Math. Struct. in .. - Judgmental.. (Correct)
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Vigan`o, L. (1997). A Framework for Non-Classical Logics. PhD thesis, Universitat des Saarlandes. Wickline, P., Lee, P., Pfenning, F., and Davies, R. (1998). Modal types as staging specifications for run-time code generation. ACM Computing Surveys, 30(3es).
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