khunaji’s tautologies in 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.

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....

Asymptotic Monadic Second-Order Logic

In this paper we introduce so-called asymptotic logics, logics that are meant to reason about weights of elements in a model in a way inspired by topology. Our main subject of study is Asymptotic Monadic Second-Order Logic over infinite words. This is a logic talking about ωwords labelled by integers. It contains full monadic second-order logic and can express asymptotic properties of integers ...

Second-order Propositional Announcement Logic

In this paper we introduce Second-order Propositional Announcement Logic (SOPAL): a language to express arbitrary announcements in Public Announcement Logic, by means of propositional quantification. We present SOPAL within a multi-agent context, and show that it is rich enough to express complex notions such as preservation under arbitrary announcements, knowability, and successfulness. We ana...

Boolean-Valued Second-Order Logic