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Formal System
Published in Masao Yokota, Natural Language Understanding and Cognitive Robotics, 2019
This chapter presents a formal system for representation and computation of human common-sense knowledge about the physical world to be employed in robotic natural language understanding. A formal system is defined as a pair of a formal language and a deductive system consisting of the axioms and inference rules employed for theorem derivation. Mental image description language (i.e., Lmd) is a formal language for many-sorted predicate logic with five types of terms specific to the mental image model. Therefore, the deductive system intended here is to be based on the deductive apparatus for predicate logic.
Formal Systems
Published in Janet Woodcock, Software Engineering Mathematics, 1988
In this short chapter we have introduced the concept of a formal system. We have seen that a formal system comprises a formal language and a deductive apparatus, and that to be useful it must be given a semantics. The notions of proofs and derivations have been introduced, and a way of presenting these has been established. We have also introduced two properties of formal systems and their interpretations, completeness and consistency.
Algebraic semantics for propositional superposition logic
Published in Journal of Applied Non-Classical Logics, 2020
A formal system K consists of a set of axioms and a set of inference rules . The axioms of K always include the axioms of PL, while includes the inference rule of PL. So let us first fix the axiomatisation for PL consisting of the following axiom schemes (for the language ). ,
Combining evolutionary computation with the variable neighbourhood search in creating an artificial music composer
Published in Connection Science, 2019
By the term of “formal system”, here we mean a well-defined system of abstract thought composed of a set of symbols as well as a collection of rules to manipulate these symbols in integrating them into meaningful formulas (compositions). In all of the examples provided, the combination of genetic algorithm and the variable neighbourhood search has been able to minimise the penalties in the level of o or 1. It is worth noting that when the penalty (anti-score) for a generated piece is 1, in the generation of that piece only one rule has been violated.