Logic, Programming and Prolog - Chapter 1 Notes

Logic Formulas

Example

In declartative form

(i) Every mother loves her children

(ii) Mary is a mother and Tome is Mary’s child

(iii) Mary loves Tom

In formalized form

What is a declarative sentence?

A declarative sentence is a complete expression of natural language which is either true or false, as opposed to e.g. imperative or interrogative sentences (commands and questions). Only declarative sentences can be expressed in predicate logic.

What is the principal idea of logic programming

To describe possibly infinite relations on objects and to apply the programming system in order to draw conclusions.

What does the alphabet of the language of predicate logic consist of?

variables:

which will be written as alphanumeric identifiers beginning with capital letters(sometimes subscriped)
constants:

which are numerals or alphanumeric identifiers beginning with lowercase letters
functors:

which are alphanumeric identifiers beginning with lower-case letters and with an associated arity greater than 0
predicate symbols:

which are usually alphanumeric identifiers starting with lowercase letters and with an associated arity greater than or equal to 0
logical connectives:

which are conjunction, negation, logical equivalence, implication and disjuction
quantifiers:

which are universal and existential
auxiliary symbols like parentheses and commas