Towards a Natural Way of Reasoning

It is well known that traditional quantifiers ∀ and ∃ are not suitable for expressing common sense rules such as ‘birds fly.’ This sentence expresses the defeasible idea that ‘most birds fly,’ and not ‘all birds fly.’ Another defeasible rule is exemplified by ‘many Americans like American football.’ Noun phrases such as ‘most birds, many birds,’ or even ‘some birds’ are recognized by semanticists as natural language generalized quantifiers. From a non-monotonic reasoning perspective, one can divide the class of linguistic generalized quantifiers into two categories. The first partition includes categorical quantifiers such as ‘all birds.’ The other one includes the defeasible quantifiers such as ‘most birds’ and ‘many birds.’ It is clear that the semantics of defeasible quantifiers leaves room for exceptions. The exceptional elements licensed by defeasible generalized quantifiers are usually the ‘non flying birds’ that non-monotonic logics deal with.