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This thesis has two aims: firstly, to explore the possibility of using probability theory to give an account of meaning (as in intension) for natural language and, secondly, to provide formal probabilistic semantics for several paraconsistent logics. The first aim results in the sketch of a probabilistic evidential role semantics for natural language, which is presented in Chapter 8. The second aim results in formal probabilistic semantics for First Degree Entailment (FDE) and the Logic of Paradox (LP) presented in Chapter 6, together with semantics for the relevant logics, B+ and B, which are presented in Chapter 7. The thesis falls in two parts. The first part, from Chapters 1-5, explores several theories of meaning for natural language with the view of identifying important concepts and lessons that can be used to develop a probabilistic account. The second part consists of Chapters 6-8 where the semantic theories are developed.
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