Information and Knowledge: a Constructive Type-Theoretical Approach

This book develops a philosophical and logical interpretation of the concept of information within the formal structure of Constructive Type Theory (CTT), in a manner concurrent with a diverse range of contemporary perspectives on the philosophy of information. On the basis of this conceptual framework, the problem of analyticity for logical derivations is faced and a solution is proposed. The text begins with a presentation of the formal structure of CTT, paying particular attention...
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This book develops a philosophical and logical interpretation of the concept of information within the formal structure of Constructive Type Theory (CTT), in a manner concurrent with a diverse range of contemporary perspectives on the philosophy of information. On the basis of this conceptual framework, the problem of analyticity for logical derivations is faced and a solution is proposed. The text begins with a presentation of the formal structure of CTT, paying particular attention to some topics that have been neglected by current researchers in Type Theory. The treatment is especially formulated for logicians with a philosophical background, but without neglecting a complete formulation of all the technicalities and formal properties. The problem of analyticity is then introduced via an historically and theoretically oriented formulation, beginning with Kant and Bolzano and following its development up to the introduction of the notion of information, extending some lines of research introduced in the contemporary debate by Hintikka. The semantical approach to information is reconsidered in the light of a constructive approach to epistemology, leading to a theoretical analysis of knowledge systems. This allows for the presentation of a formal structure, based on certain typical operations in the formalization of CTT and the use of formal properties of Kripke models, in which the notions of information and knowledge are defined as epistemically different. These definitions involve an extension of constructive epistemology, bringing new material to the extremely open range of problems determined by the notion of verification and the related theory of meaning. Information and Knowledge presents a new interesting perspective on the constructive interpretation of knowledge processes, suggesting the reliability of such an approach for the logical modeling of epistemic problems and proposing a unifying frame from one of the more important contemporary philosophical perspectives.