By Antoni Ligeza
The ebook offers logical foundations for rule-based platforms. An try has been made to supply an in-depth dialogue of logical and different facets of such structures, together with languages for wisdom illustration, inference mechanisms, inference keep watch over, layout and verification. the last word objective used to be to supply a deeper theoretical perception into the character of rule-based platforms and prepare the main whole presentation together with info so usually skipped in commonplace textbooks. The booklet should be valuable to in all probability huge viewers, however it is aimed toward offering particular wisdom for graduate, post-graduate and Ph.D. scholars, in addition to wisdom engineers and learn staff considering the area of AI. It additionally constitutes a precis of the Author’s learn and event collected via a number of years of his examine paintings.
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Additional resources for Logical Foundations for Rule-Based Systems
Let p1 , p2 , . . , pk be some positive literals and let h be any literal (either positive or negative). Any formula of the form ψ = ¬p1 ∨ ¬p2 ∨ . . 9) will be called a Horn clause. A Horn clause is one containing at most one positive literal. e. p1 ∧ p2 ∧ . . ∧ pk ⇒ h . 9). Such rules constitute an important form for knowledge representation — they constitute the core of logic programming and rule-based systems. Any clause can be considered as a set of its literals. Then it may be convenient to apply the set notation directly to its elements.
Last but not least, variables play the role of coreference constraints and data carriers. Two or more occurrences of the same variable in an expression denote the same object; if any replacement of an occurrence of some variable takes place, all the occurrences of this variable must be replaced with the same symbol or value. In this way data may be passed from rule input to output of the rule — a variable occurring in preconditions and conclusion of a rule will carry its value over the rule after being uniﬁed with some values during matching of preconditions against current state formula.
However, note that such an approach may lead to certain problems concerning automated reasoning, if no auxiliary rules (deﬁning all the interdependencies among facts) are deﬁned. For example, no purely logical inference engine will be capable of stating that a formula like switch on ∧ switch off is always false2 — in such a case an auxiliary reasoning rule like, for example, switch on ⇒ ¬switch off should be provided so as to assure the detection of inconsistency. To summarize, any two complementary literals p and ¬p satisfy the following properties: |= p ∨ ¬p and |= p ∧ ¬p .
Logical Foundations for Rule-Based Systems by Antoni Ligeza