Related papers: Structural Refinement for the Modal nu-Calculus
This article shows a correspondence between abstract interpretation of imperative programs and the refinement calculus: in the refinement calculus, an abstract interpretation of a program is a specification which is a function. This…
Refinement types are types equipped with predicates that specify preconditions and postconditions of underlying functional languages. We propose a general semantic construction of dependent refinement type systems from underlying type…
We establish a novel connection between two research areas in non-classical logics which have been developed independently of each other so far: on the one hand, input/output logic, introduced within a research program developing logical…
This paper is a contribution to the search for efficient and high-level mathematical tools to specify and reason about (abstract) programming languages or calculi. Generalising the reduction monads of Ahrens et al., we introduce transition…
In an article dating back in 1992, Kosta Do\v{s}en initiated a project of modal translations in substructural logics, aiming at generalizing the well-known G\"{o}del-McKinsey-Tarski translation of intuitionistic logic into {\bf S4}.…
In this work, we tackle model efficiency by exploiting redundancy in the \textit{implicit structure} of the building blocks of convolutional neural networks. We start our analysis by introducing a general definition of Composite Kernel…
Fusions are a simple way of combining logics. For normal modal logics, fusions have been investigated in detail. In particular, it is known that, under certain conditions, decidability transfers from the component logics to their fusion.…
We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…
This paper studies the complexity of classical modal logics and of their extension with fixed-point operators, using translations to transfer results across logics. In particular, we show several complexity results for multi-agent logics…
We explore the theory of illfounded and cyclic proofs for the propositional modal $\mu$-calculus. A fine analysis of provability for classical and intuitionistic modal logic provides a novel bridge between finitary, cyclic and illfounded…
This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we…
We present an extension of an algorithm for computing directly the denotation of a mu-calculus formula X over the configuration graph of a pushdown system to allow backwards modalities. Our method gives the first extension of the saturation…
We introduce a formalism to analyze partially defined functions between ordered sets. We show that our construction provides a uniform and conceptual approach to all the main definitions encountered in elementary real analysis including…
We present a novel approach to construction of a formal semantics for a programming language. Our approach, using a parametric denotational semantics, allows the semantics to be easily extended to support new language features, and…
Though modern neural networks have achieved impressive performance in both vision and language tasks, we know little about the functions that they implement. One possibility is that neural networks implicitly break down complex tasks into…
We prove a theorem stating that any semantics can be encoded as a compositional semantics, which means that, essentially, the standard definition of compositionality is formally vacuous. We then show that when compositional semantics is…
Session types capture precise protocol structure in concurrent programming, but do not specify properties of the exchanged values beyond their basic type. Refinement types are a form of dependent types that can address this limitation,…
Structured neuron encapsulation introduces a modular framework that enables more effective aggregation and specialization of information within deep learning architectures. A model modified through this framework demonstrated improved…
We describe two ``semantically-oriented'' dependency-structure formalisms, U-forms and S-forms. U-forms have been previously used in machine translation as interlingual representations, but without being provided with a formal…
Natural language semantics has recently sought to combine the complementary strengths of formal and distributional approaches to meaning. More specifically, proposals have been put forward to augment formal semantic machinery with…