In forward chaining systems as individual facts are added to the knowledge base, modus pones is used to fire all applicable implication rues. The process continues until no further facts can be deduced. The disadvantage of this approach is that facts that will never be needed may be inferred and stored.

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Modus ponens is the most widely implemented inference method provided by FOL. It functions by corresponding to what is informally known as if-then reasoning. Thus, if the left-hand side of an implication rule is true, then the right-hand side of the rule can be inferred.

Modus Ponens

An on-going but a helpful book resource about NLP
https://web.stanford.edu/~jurafsky/slp3/

Speech and Language Processing (3rd ed. draft) 

Forward Chaining 

In backward chaining modus ponens is run in reverse to prove specific propositions called queries. However while backward chaining is a sound method of reasoning, reasoning backwards is an invalid form of plausible reasoning.

Backward Chaining 

An alternative inference technique that is sound and complete (unlike forward and backward reasoning only being sound). Unfortunately, inference systems based on resolution are far more computationally expensive.

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