A logical approach in information theory

Baimuratov I.R., Zhukova N.A.

ITMO University

As logical approach in information theory we suppose an approach, where data is considered as logical objects and information – as property of logical objects. The purpose of developing this new approach is logic and information theory development. To achieve this goal, we did a research and got a number of results.

The first result is an explanation of existing three different historical approaches in information theory: communicative (C. Shannon), semantic (Y. Bar-Hillel, R. Carnap) and algorithmic (G. Chaitin, A. Kolmogorov, R. Solomonoff). The explanation is that logical objects can be considered from different perspectives: syntactic, semantic and deductive. Therefore, communicative approach is associated with syntax of logical objects, semantic approach – with semantics and algorithmic approach – with deduction.

The second result is strict definition and logical classification of data processing methods according to logical relations they correspond. First order predicate logic is used as logical system, sufficient to set the correspondence. It has three types of logical functions: individual, predicate and propositional. Therefore, all data processing methods can be divided into three logical kinds referred as individual, predicate and propositional data processing.

Further, applying methods of communicative, semantic and algorithmic approaches to syntactic, semantic and deductive properties of logical objects, we are able to define information characteristics for different logical relations. Consider semantic informativeness in details. As semantic properties of logical relations we suppose interpretation and valuation functions for expressions of logical language that denote these relations. As semantic approach in information theory we suppose an approach where random variables are considered as information bearers, informativeness of random variables is defined as its entropy and informativeness of its variables – as self-information. Therefore, it is able to define semantic informativeness of individual, predicate and propositional functions.

To sum up, the logical approach in information theory appears to be reasonable. The results for information theory include more formal definitions of basic notions and foundation of the theory on logical basement in general, for logic – in defining of information characteristics for different logical relations.

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