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John Pollock's OSCAR system [2] is an example of an automated argumentation system that is more specific than being just an automated theorem prover. Tools and techniques of automated reasoning include the classical logics and calculi, fuzzy logic, Bayesian inference, reasoning with maximal entropy and many less formal ad hoc techniques.
An example of backward chaining. If X croaks and X eats flies – Then X is a frog; If X chirps and X sings – Then X is a canary; If X is a frog – Then X is green; If X is a canary – Then X is yellow; With backward reasoning, an inference engine can determine whether Fritz is green in four steps.
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major motivating factor for the development of computer science .
Drools, a forward-chaining inference-based rules engine which uses an enhanced implementation of the Rete algorithm. Evrete, a forward-chaining Java rule engine that uses the Rete algorithm and is compliant with the Java Rule Engine API (JSR 94). D3web, a platform for knowledge-based systems (expert systems).
Another example general problem solver was the SOAR family of systems. In practice these theorem provers and general problem solvers were seldom useful for practical applications and required specialized users with knowledge of logic to utilize. The first practical application of automated reasoning were expert systems. Expert systems focused ...
A trivial example of how this rule would be used in an inference engine is as follows. In forward chaining, the inference engine would find any facts in the knowledge base that matched Human(x) and for each fact it found would add the new information Mortal(x) to the knowledge base. So if it found an object called Socrates that was human it ...
The resulting inference rule is refutation-complete, [6] in that a set of clauses is unsatisfiable if and only if there exists a derivation of the empty clause using only resolution, enhanced by factoring. An example for an unsatisfiable clause set for which factoring is needed to derive the empty clause is:
For example, non-monotonic reasoning could be used with truth maintenance systems. A truth maintenance system tracked assumptions and justifications for all inferences. It allowed inferences to be withdrawn when assumptions were found out to be incorrect or a contradiction was derived.