Remarks on Type Theory in the Semantics of Propositional Attitudes

Abstract

The article contains concise comments on issues addressed in responses to the article “Type theory in the semantics of propositional attitudes”. I agree that the opening paper suggests no new solutions for problems of propositional attitudes. It aims at developing a method of their more convenient and effective description. Type theory is more expressive in comparison with many traditional approaches. I also agree that the connection between this approach and operations of epistemic subject needs further clarification. However, this disadvantage belongs not to Martin-Löf’s theory itself but to the approach chosen by me. As regards to the intuitinism of type theory, it does not need to be intuitionistic in its logic, but for semantics it is important for it to preserve the constructivist character. Relations between type theory and intensional logic also call for clarification. It seems that it is rather closer to situation semantics. The criticism by E. Borisov and A. Rodin reveals problems of the concept of the context relation function. The chief result of the discussion is the awarenness that means similar to conterpart relations are more appropriate here than this function.