Related papers: Elements of affine model theory

In recent work, comonads and associated structures have been used to analyse a range of important notions in finite model theory, descriptive complexity and combinatorics. We extend this analysis to Hybrid logic, a widely-studied extension…

This paper introduces an abstract notion of fragments of monadic second-order logic. This concept is based on purely syntactic closure properties. We show that over finite words, every logical fragment defines a lattice of languages with…

We study the fluted fragment of first-order logic which is often viewed as a multi-variable non-guarded extension to various systems of description logics lacking role-inverses. In this paper we show that satisfiable fluted sentences (even…

Optimization layers in deep neural networks have enjoyed a growing popularity in structured learning, improving the state of the art on a variety of applications. Yet, these pipelines lack interpretability since they are made of two opaque…

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…

We combine continuous and integral logics and found a logical framework for metric measure spaces equipped with a family of continuous relations and operations. We prove the ultraproduct theorem and deduce compactness and other usual…

Ultrafinitism postulates that we can only compute on relatively short objects, and numbers beyond certain value are not available. This approach would also forbid many forms of infinitary reasoning and allow to remove certain paradoxes…

Orthogonality is a notion based on the duality between programs and their environments used to determine when they can be safely combined. For instance, it is a powerful tool to establish termination properties in classical formal systems.…

The paper is devoted to construction of some closed inductive sequence of models of the generalized second-order Dedekind theory of real numbers with exponentially increasing powers. These models are not isomorphic whereas all models of the…

Refinement transforms an abstract system model into a concrete, executable program, such that properties established for the abstract model carry over to the concrete implementation. Refinement has been used successfully in the development…

We want to propose a new discretization ansatz for the second order Hessian complex exploiting benefits of isogeometric analysis, namely the possibility of high-order convergence and smoothness of test functions. Although our approach is…

Ordered logics and type systems have been used in a variety of applications including computational linguistics, memory allocation, stream processing, logical frameworks, parametricity, and enforcing security protocols. In most…

Proof-theoretic methods are developed for subsystems of Johansson's logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are exploited to establish properties of the logical systems.…

We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…

We consider weighted structures, which extend ordinary relational structures by assigning weights, i.e. elements from a particular group or ring, to tuples present in the structure. We introduce an extension of first-order logic that allows…

We present an affine-intuitionistic system of types and effects which can be regarded as an extension of Barber-Plotkin Dual Intuitionistic Linear Logic to multi-threaded programs with effects. In the system, dynamically generated values…

We present an affine-intuitionistic system of types and effects which can be regarded as an extension of Barber-Plotkin Dual Intuitionistic Linear Logic to multi-threaded programs with effects. In the system, dynamically generated values…

In a previous publication, we introduced an abstract logic via an abstract notion of quantifier. Drawing upon concepts from categorical logic, this abstract logic interprets formulas from context as subobjects in a specific category, e.g.,…

This paper develops a categorical framework to clarify the relationship between the completeness and compactness theorems in classical first-order logic. Rather than claiming that different model constructions yield naturally isomorphic…

We investigate four model-theoretic tameness properties in the context of least fixed-point logic over a family of finite structures. We find that each of these properties depends only on the elementary (i.e., first-order) limit theory, and…