Related papers: Continuous logic in a classical setting

We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…

We provide a general framework for the study of valuations on Banach lattices. This complements and expands several recent works about valuations on function spaces, including $L_p(\mu)$, Orlicz spaces and spaces $C(K)$ of continuous…

Hilbert's Entscheidungsproblem has given rise to a broad and productive line of research in mathematical logic, where the classification process of decidable classes of first-order sentences represent only one of the remarkable results.…

Using the category of metric spaces as a template, we develop a metric analogue of the categorical semantics of classical/intuitionistic logic, and show that the natural notion of predicate in this "continuous semantics" is equivalent to…

We study the complexity of the model checking problem, for fixed model A, over certain fragments L of first-order logic. These are sometimes known as the expression complexities of L. We obtain various complexity classification theorems for…

We introduce a fragment of continuous first-order logic, analogue of Palyutin formulas (or h-formulas) in classical model theory, which is preserved under reduced products in both directions. We use it to extend classical results on…

It is well known that many-sorted logic can be reduced to unsorted first-order logic by adding predicates for each sort, relativizing quantifiers to these predicates, and adding appropriate axioms governing their behavior. Existing…

We study the basic properties of a dual "spectral" topology on positive type spaces of h-inductive theories and its essential connection to infinitary logic. The topology is Hausdorff, has the Baire property, and its compactness…

In computer science, various logical languages are defined to analyze properties of systems. One way to pinpoint the essential differences between those logics is to compare their expressivity in terms of distinguishing power and expressive…

In the affine fragment of continuous logic, type spaces are compact convex sets. I study some model theoretic properties of extreme types. It is proved that every complete theory $T$ has an extremal model, i.e. a model which realizes only…

The existence of a Banach limit as a translation invariant positive continuous linear functional on the space of bounded scalar sequences which is equal to 1 at the constant sequence (1,1,...,1,...) is proved in a first course on functional…

Local-order-invariant (first-order) logic is an extension of first-order logic where formulae have access to a ternary local order relation on the Gaifman graph, provided that the truth value does not depend on the specific order relation…

We prove existence of wide types in a continuous theory expanding a Banach space, and density of minimal wide types among stable types in such a theory. We show that every minimal wide stable type is "generically" isometric to an l_2 space.…

This paper seeks to apply categorical logic to the design of artificial intelligent agents that reason symbolically about objects more richly structured than sets. Using Johnstone's sequent calculus of terms- and formulae-in-context, we…

We establish complete characterizations of various notions of expansivity for weighted composition operators on a very general class of locally convex spaces of continuous functions. This class includes several classical classes of…

There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions…

We consider a language together with the subword relation, the cover relation, and regular predicates. For such structures, we consider the extension of first-order logic by threshold- and modulo-counting quantifiers. Depending on the…

We study relationship between first order multiplicative linear logic (MLL1), which has been known to provide representations to different categorial grammars, and the recently introduced extended tensor type calculus (ETTC). We identify a…

We study $\varepsilon$-stability in continuous logic. We first consider stability in a model, where we obtain a definability of types result with a better approximation than that in the literature. We also prove forking symmetry for…

We begin the study of categorical logic for continuous model theory. In particular, we 1. introduce the notions of metric logical categories and functors as categorical equivalents of a metric theory and interpretations, 2. prove a…