[FOM] Free logic

[Tennant, Neil]

A sound and complete first-order system of universally free logic can be found in Chapter 7 of my book Natural Logic  (EUP, 1978; 2nd revised edn. 1990), which is available as a free download at http://u.osu.edu/tennant.9/publications/
It handles non-denoting names; partial functions; definite descriptions; set abstraction terms; number-abstraction terms---indeed, any kind of singular term that might fail to denote. It is set out as a Gentzen-Prawitz system of natural deduction. The only extensions or modifications needed to pass from the usual non-free logic to the free logic are:
(i) a rule of atomic denotation;
(ii) a rule of functional denotation;
(iii) and the obvious 'existential presuppositions' for terms and parameters involved in the quantifier rules.
This logic can handle the formalization of any branch of mathematical reasoning at first order.
Neil Tennant

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