We give several characterizations of when a complete first-order theory T T is monadically NIP, i.e. expansions by arbitrary unary pred...

Pioneers of logic, among them J.R. Büchi, M.O. Rabin, S. Shelah, and Y. Gurevich, have shown that monadic second-order logic offers a rich landscape of interesting decidable theories. Prominent examples are the monadic theory of the successor structure S1 = (N,+1) of the natural numbers and the monadic theory of the binary tree, i.e., of the two-successor structure S2 = ({0, 1} ∗, ·0, ·1). We c...

The main purpose of this work is to introduce the class of the monadic dynamic algebras (dynamic algebras with one quantifier). Similarly to a theorem of Kozen we establish that every separable monadic dynamic algebra is isomorphic to a monadic (possibly non-standard) Kripke structure. We also classify the simple (monadic) dynamic algebras. Moreover, in the dynamic duality theory, we analyze th...

Let M = (A,<, P ) where (A,<) is a linear ordering and P denotes a finite sequence of monadic predicates on A. We show that if A contains an interval of order type ω or −ω, and the monadic second-order theory of M is decidable, then there exists a non-trivial expansion M ′ of M by a monadic predicate such that the monadic second-order theory of M ′ is still decidable.

In this paper, we propose a monadic higher order safe ambient calculus. The expressiveness of this calculus is studied. We showed that polyadic higher order safe ambient calculus, first order safe ambient calculus with capability-passing, first order safe ambient calculus with name-passing, and polyadic π-calculus can all be encoded in monadic higher order ambient calculus. At last, we show tha...

Short cut fusion improves the efficiency of modularly constructed programs by eliminating intermediate data structures produced by one program component and immediately consumed by another. We define a combinator which expresses uniform production of data structures in monadic contexts, and is the natural counterpart to the well-known monadic fold which consumes them. Like the monadic fold, our...

To any finite group G SL2ðCÞ and each element t in the center of the group algebra of G, we associate a category, CohðP G;t ;PÞ: It is defined as a suitable quotient of the category of graded modules over (a graded version of) the deformed preprojective algebra introduced by Crawley-Boevey and Holland. The category CohðP G;t ;PÞ should be thought of as the category of coherent sheaves on a ‘non...

A predicate logic of probability, close to logics of probability of Halpern and al., is introduced. Our main result concerns the following model-checking problem: deciding whether a given formula holds on the structure defined by a given Finite Probabilistic Process. We show that this model-checking problem is decidable for a rather large subclass of formulas of a second-order monadic logic of ...