An axiom system for the weak monadic second order theory of two successors

An Axiom System For the Weak Monadic Second Order Theory of Two Successors

A complete axiom system for the weak monadic second order theory of two successor funct ions , W2S , is presen ted . The axiom system consists , rough ly , of the general ized Peano axioms and of an inductile defini t ion of the fini te sets . For the proof , methods of J . R . Buchi and J . Doner are used to obtain a new decision procedure for W2S , whose proofs are easi ly formal ized . Diffe...

Deciding Weak Monadic Second-order Logics using Complex-value Datalog

In this paper we propose to use techniques developed for query evaluation of Complex-value Datalog queries for determining satisfiability of WS1S and WS2S formulæ. This in turn can serve as a decision procedure for Description Logics for which embeddings into WS1S and WS2S have been proposed recently. We show that the use of database query evaluation techniques—in particular the Magic Set rewri...

Definability in the Monadic Second-Order Theory of Successor

The Monadic Second-Order Theory of Ordinals w sub 2

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 ...