Presentation of proofs in modal natural deduction

E. de Lima
2000 Journal of Logic and Computation  
We introduce a calculus for transforming first-order proofs of theorems originally formulated in modal logic, into modal natural deduction proofs. With a transformation procedure based on this calculus, we are able to present a proof in the language in which the problem was originally formulated, and in a formalism giving better insight into the contents of the proof. As a target language of the proof transformation we use a linearized modal natural deduction calculus which makes the reasoning
more » ... akes the reasoning involving modal contexts explicit. We define a substitution as a mapping from ¥ to ¥ such that for Ò, ´ µ ´ ½µ AE AE ´ Òµ. We say ¼ is an instance of if there is a substitution such that ´ µ ¼ . Further, we say two world paths are unifiable if they have a common instance.
doi:10.1093/logcom/10.4.527 fatcat:65uxc5ornbfslocepkn4mcpztq