A major result concerning Temporal Logics (TL) is Kamp’s theorem [Kam68, GHR94], which states that the temporal logic over the pair of modalities X until Y and Xsince Y is expressively complete for the first order fragment of monadic logic of order over the natural numbers. We show that there is no finite set of modalities B such that the temporal logic over B and monadic logic of order have th...

Using contextual equivalence (a.k.a. observational equivalence) to specify security properties is an important idea in the field of formal verification of cryptographic protocols. While contextual equivalence is difficult to prove directly, one is usually able to deduce it using so-called logical relations in typed λ-calculi. We apply this technique to the cryptographic metalanguage — an extens...

A monadic (Boolean) algebra is a Boolean algebra A together with an operator 3 on A (called an existential quantifier, or, simply, a quantifier) such that 30=0, pfk 3p, and 3(^A 3q) = 3p* 3g whenever p and q are in A. Most of this note uses nothing more profound about monadic algebras than the definition. The reader interested in the motivation for and the basic facts in the theory of monadic a...

Cost monadic logic extends monadic second-order logic with the ability to measure the cardinal of sets. In particular, it allows to decide problems related to boundedness questions. In this paper, we provide new decidability results allowing the systematic investigation of questions involving “relative boundedness”. The first contribution in this work is to introduce a suitable logic for such q...

In this paper, we study several sublogics of monadic secondorder logic over countable linear orderings, such as first-order logic, firstorder logic on cuts, weak monadic second-order logic, weak monadic second-order logic with cuts, as well as fragments of monadic secondorder logic in which sets have to be well ordered or scattered. We give decidable algebraic characterizations of all these log...

We will show that Banach spaces are (a) monadic over complete metric via the unit ball functor and (b) pointed forgetful functor.

We study monadic translations of the call-by-name (cbn) and the call-by-value (cbv) fragments of the classical sequent calculus λμμ̃ by Curien and Herbelin and give modular and syntactic proofs of strong normalization. The target of the translations is a new meta-language for classical logic, named monadic λμ. It is a monadic reworking of Parigot’s λμ-calculus, where the monadic binding is confi...

Closed monadic Σ1, as proposed in [AFS98], is the existential monadic second order logic where alternation between existential second order quantifiers and first order quantifiers is allowed. Despite some effort very little is known about the expressive power of this logic on finite structures. We construct a tree automaton which exactly characterizes closed monadic Σ1 on the Rabin tree and giv...

Modular monadic semantics can be implemented using folds or catamorphisms over a functor that expresses the abstract syntax of the language. By composing several functors, it is possible to obtain modular interpreters from reusable components. Monadic folds structure programs that process recursively their input and control the side effects of the output they produce. We consider that the seman...