Abstract: Within the binary signal detection theory (BSDT) the semantics and syntax of a primary language (PL, a mathematical framework for internal brain computations) have been proposed and described in a semi-formal form. On the basis of BSDT infinity hypothesis (the infinity of common in the past prehistory of universe, life, and mind), basic BSDT PL notions have been defined. Among them the names of real-world things, their meanings/contexts (they are infinite and common in the past binary strings), meaning complexity, truth, and understanding the truth. Given their infinite contexts BSDT PL names are finite-in-length binary strings that may simultaneously be interpreted as Gödel numbers or uncomputable halting probabilities (fractions of Chaitin’s Ω) for binary string algorithms running on particular self-delimiting computers. BSDT PL meaning complexity is compared with Shannon entropy/information, Kolmogorov/algorithmic complexity, Gell-Mann? and Lloyd’s effective complexity and total information; BSDT PL truth is compared with Tarskian truth. High biological plausibility of the BSDT PL, its potential for disigning the languages with capacities at the level of human natural languages, applications to practical semantic computations and testable empirical predictions are discussed. Because of its infinity hypothesis, BSDT PL is beyond the scope of traditional axiomatic approach to logic and mathematics.

Keywords: meaning, complexity, truth, symbolic communications, semantic computations.

ACM Classification Keywords: C.3 Special-purpose and Application-based Systems; E.4 Coding and Information Theory; F.1.3 Complexity Measures and Classes; H.1.1 Systems and Information Theory; I.2.0 General, I.2.4 Knowledge Representation Formalisms and Methods; J.4 Social and Behavioral Sciences

Link:

ON SEMANTICS AND SYNTAX OF THE BSDT PRIMARY LANGUAGE

Petro Gopych

http://foibg.com/ibs_isc/ibs-19/ibs-19-p15.pdf