Entities supposed to make propositions or sentences true are called truthmakers.A classification of truthmakers into exact and inexact ones is proposed by Kit Fine in his "truthmaker" semantics : the former are truthmakers "wholly relevant" to propositions in terms of truthmaking, while the latter may be not. Fine demonstrates that the exact notion of truthmaking is often useful to provide fine-grained analysis of philosophical-logical and other various issues.
In this paper, we apply the exact notion of truthmaking to linear logic and outline a truthmaker interpretation of its semantics. We take states of affairs as truthmakers and interpret Girard's phase semantics, a model-theoretic (Tarskian) semantics of linear logic, in terms of states of affairs. Putting the "state space" structure in Fine's truthmaker semantics together with the "phase space" structure in phase semantics, we obtain models for classical linear logic in the style of truthmaker semantics. We put forth some truthmaker views on the models and the connectives of linear logic including exponential modalities.

特集 : 岡田光弘教授 退職記念号
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