Related papers: Recursive axiomatisations from separation properti…
In this note we axiomatize the classes of rudimentary functions, primitive recursive functions, safe recursive set functions, and predicatively computable functions.
In this paper we provide purely model-theoretic (algebraic) characterisations for classes definable in second-order logic and for pseudo-elementary classes (including PC and PC_{\Delta} classes). Classical results of this flavour include…
This paper studies the logical properties of a very general class of infinite ranked trees, namely those generated by higher-order recursion schemes. We consider, for both monadic second-order logic and modal mu-calculus, three main…
We define the adjacent fragment AF of first-order logic, obtained by restricting the sequences of variables occurring as arguments in atomic formulas. The adjacent fragment generalizes (after a routine renaming) two-variable logic as well…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
The aim of this paper is to propose a many-valued modal framework to formalize reasoning with both graded preferences and propositions, in the style of van Benthem et al.'s classical modal logics for preferences. To do so, we start from Bou…
First-order logic is known to have limited expressive power over finite structures. It enjoys in particular the locality property, which states that first-order formulae cannot have a global view of a structure. This limitation ensures on…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
Abstract separation systems are a new unifying framework in which separations of graph, matroids and other combinatorial structures can be expressed and studied. We characterize the abstract separation systems that have representations as…
We identify a number of decidable and undecidable fragments of first-order concatenation theory. We also give a purely universal axiomatization which is complete for the fragments we identify. Furthermore, we prove some normal-form results.
We show that a partial-correctness assertion about an iterative program is provable in Hoare Logic iffit is provable in standard second-order logic with comprehension restricted to first-order predicates. This equivalence was claimed twice…
We deal with various splitting methods in algebraic logic. The word `splitting' refers to splitting some of the atoms in a given relation or cylindric algebra each into one or more subatoms obtaining a bigger algebra, where the number of…
First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies…
Separation logic is a concise method for specifying programs that manipulate dynamically allocated storage. Partially inspired by separation logic, Implicit Dynamic Frames has recently been proposed, aiming at first-order tool support. In…
We investigate the representation and complete representation classes for algebras of partial functions with the signature of relative complement and domain restriction. We provide and prove the correctness of a finite equational…
This article provides an algebraic study of intermediate inquisitive and dependence logics. While these logics are usually investigated using team semantics, here we introduce an alternative algebraic semantics and we prove it is complete…
Regular synchronization languages can be used to define rational relations of finite words, and to characterize subclasses of rational relations, like automatic or recognizable relations. We provide a systematic study of the decidability of…