| A Variant of Thomason's First-order Logic CF Based on Situations (1998) | |||||||||||||||
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| In this paper, we define a first-order logic CF 0 with strong negation and bounded static quantifiers, which is a variant of Thomason's logic CF . For the logic CF 0 , the usual Kripke formal semantics is defined based on situations, and a sound and complete axiomatic system is established based on the axiomatic systems of constructive logics with strong negation and Thomason's completeness proof techniques. With the use of bounded quantifiers, CF 0 allows the domain of quantification to be empty and allows for non-denoting constants. CF 0 is intended as a fragment of a logic for situation theory. Thus the connection between CF 0 and infon logic is discussed. 1 Introduction Thomason [26] constructed a first-order logic CF . In his logic, a constructive negation is used instead of a classical or intuitionistic one. Constructive negation, also called strong negation, was introduced by Nelson [22] following Kleene's notion of recursive realizability, emphasising that false nu... | |||||||||||||||
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