Propositional Logic Syntax Acquisition Using Induction and Self-Organisation

Propositional Logic Syntax Acquisition Using Induction and Self-Organisation

Josefina Sierra (Universidad Politécnica de Cataluña, Spain) and Josefina Santibáñez (Universidad de La Rioja, Spain)
DOI: 10.4018/978-1-60566-236-7.ch013
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Abstract

This chapter addresses the problem of the acquisition of the syntax of propositional logic. An approach based on general purpose cognitive capacities such as invention, adoption, parsing, generation, and induction is proposed. Self-organisation principles are used to show how a shared set of preferred lexical entries and grammatical constructions, that is, a language, can emerge in a population of autonomous agents which do not have any initial linguistic knowledge. Experiments in which a population of autonomous agents constructs a grammar that allows communicating the formulas of a propositional logic language are presented. These experiments extend previous work by considering a larger population and a much larger search space of grammar rules. In particular, the agents are allowed to order the expressions associated with the constituents of a logical formula in arbitrary order. Previous work assumed that the expressions associated with the connectives should be placed in the first position of the sentence.
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Grammatical Formalism

We use a restricted form of Definite Clause Grammar in which non-terminals have three arguments attached to them. The first argument conveys semantic information. The second is a score in the interval [0, 1] that estimates the usefulness of that association in previous communication. The third argument is a counter that records the number of times the association has been used in previous language games.

Many grammars can be used to express the same meaning. The following holistic grammar can be used to express the propositional formula right∧light.

  • s([and, right, light]), 0.01) → andrightlight

  • (1)

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