Boolean-Valued Second-Order Logic

Boolean-Valued Second-Order Logic

Second-Order Equational Logic

We provide an extension of universal algebra and its equational logic from first to second order. Conservative extension, soundness, and completeness results are established.

khunaji’s tautologies in second-order logic

for the first time in the history of logic, afzal al-din al-khunaji has found tautologies and contradictories among the verity and actuality propositions. these have been formalized and investigated in first-order logic and it has been shown that their perpetual truth requires the assumption of ‘the presupposed existence of non-existence.’ in this paper, i investigate the tautologies in second-...

First-Order Logic, Second-Order Logic, and Completeness

Both firstand second-order logic (FOL and SOL, respectively) as we use them today were arguably created by Frege in his Begriffsschrift – if we ignore the notational differences. SOL also suggests itself as a natural, and because of its much greater strength, desirable extension of FOL. But at least since W. V. Quine’s famous claim that SOL is “set theory in sheep’s clothing” it is widely held ...

Extensionalizing Intensional Second-Order Logic

Neo-Fregean approaches to set theory, following Frege, have it that sets are the extensions of concepts, where concepts are the values of second-order variables. e idea is that, given a second-order entity X, there may be an object εX, which is the extension of X. Other writers have also claimed a similar relationship between second-order logic and set theory, where sets arise from pluralities....