Related papers: Logical metatheorems for accretive and (generalize…
Logical specifications play a key role in the formal analysis of behavioural models. Automating the derivation of such specifications is particularly valuable in complex systems, where manual construction is time-consuming and error-prone.…
We present a straightforward embedding of quantified multimodal logic in simple type theory and prove its soundness and completeness. Modal operators are replaced by quantification over a type of possible worlds. We present simple…
We address the problems of computing operator norms of matrices induced by given norms on the argument and the image space. It is known that aside of a fistful of "solvable cases," most notably, the case when both given norms are Euclidean,…
Monads are of interest both in semantics and in higher dimensional algebra. It turns out that the idea behind usual notion finitary monads (whose values on all sets can be computed from their values on finite sets) extends to a more general…
We study a conical extension of averaged nonexpansive operators and the role it plays in convergence analysis of fixed point algorithms. Various properties of conically averaged operators are systematically investigated, in particular, the…
Iterative abstraction refinement techniques are one of the most prominent paradigms for the analysis and verification of systems with large or infinite state spaces. This paper investigates the changes of truth values of system properties…
A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…
This paper focuses on vector-valued composite functionals, which may be nonlinear in probability. Our primary goal is to establish central limit theorems for these functionals when mixed estimators are employed. Our study is relevant to the…
We characterize the equational theories and Lawvere theories that correspond to the categories of analytic and polynomial monads on Set, and hence also the categories of the symmetric and rigid operads in Set. We show that the category of…
Monotone operators, especially in the form of subdifferential operators, are of basic importance in optimization. It is well known since Minty, Rockafellar, and Bertsekas-Eckstein that in Hilbert space, monotone operators can be understood…
Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…
Agentic theorem provers combine a reasoning model, retrieval, search, and a proof assistant verifier, yet it remains unclear which components actually improve finite-budget proof success and why they help on real mathematical workloads. We…
The syntactic nature of logic and computation separates them from other fields of mathematics. Nevertheless, syntax has been the only way to adequately capture the dynamics of proofs and programs such as cut-elimination, and the finiteness…
We introduce proper display calculi for basic monotonic modal logic, the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…
Describing systems in terms of choices and their resulting costs and rewards offers the promise of freeing algorithm designers and programmers from specifying how those choices should be made; in implementations, the choices can be realized…
We consider a class of monotone operators which are appropriate for symbolic representation and manipulation within a computer algebra system. Various structural properties of the class (e.g., closure under taking inverses, resolvents) are…
In the refinement calculus, monotonic predicate transformers are used to model specifications for (imperative) programs. Together with a natural notion of simulation, they form a category enjoying many algebraic properties. We build on this…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
Several aspects of the interplay between monotone operator theory and convex optimization are presented. The crucial role played by monotone operators in the analysis and the numerical solution of convex minimization problems is emphasized.…
Weighted monadic second-order logic is a weighted extension of monadic second-order logic that captures exactly the behaviour of weighted automata. Its semantics is parameterized with respect to a semiring on which the values that weighted…