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 ...

The Ordered conjecture of Kolaitis and Vardi asks whether xed point logic di ers from rst order logic on every in nite class of nite ordered structures In this paper we develop the tool of bounded variable element types and illustrate its application to this and the orig inal conjectures of McColm which arose from the study of inductive de nability and in nitary logic on pro cient classes of ni...

We study three kinds of compactness in some variants of G"{o}del logic: compactness,entailment compactness, and approximate entailment compactness.For countable first-order underlying language we use the Henkinconstruction to prove the compactness property of extensions offirst-order g logic enriched by nullary connective or the Baaz'sprojection connective. In the case of uncountable first-orde...

A logic network to produce the sequency ordered Hadamard matrix H based on the property of gray code and orthogonal group codes is developed. The network uses a counter to generate Rademacher function such that the output of H will be in sequency. A general purpose shift register with output logic is used to establish a sequence of period P corresponding to a given value of order m of the Hadam...

The word 'logic' in the title of this chapter is ambiguous. In its first meaning, a logic is a collection of closely related artificial languages. There are certain languages called first-order languages, and together they form first-order logic. In the same spirit, there are several closely related languages called modal languages, and together they form modal logic. Likewise second-order logi...