相关论文: Constructive Modalities with Provability Smack

Model theoretic results such as Characterization and Definability give important information about different logics. It is well known that the proofs of those results for several modal logics have, somehow, the same 'taste'. A general proof…

Many moduli spaces are constructed as quotients of group actions; this paper surveys the classical theory, as well as recent progress and applications. We review geometric invariant theory for reductive groups and how it is used to…

We extend the meet-implication fragment of propositional intuitionistic logic with a meet-preserving modality. We give semantics based on semilattices and a duality result with a suitable notion of descriptive frame. As a consequence we…

Computation nowadays is becoming inherently concurrent, either because of characteristics of the hardware (with multicore processors becoming omnipresent) or due to the ubiquitous presence of distributed systems (incarnated in the…

In this paper we study frame definability in finitely-valued modal logics and establish two main results via suitable translations: (1) in finitely-valued modal logics one cannot define more classes of frames than are already definable in…

Inspired from human cognition, machine learning systems are gradually revealing advantages of sparser and more modular architectures. Recent work demonstrates that not only do some modular architectures generalize well, but they also lead…

We propose an explanatory and computational theory of transformative discoveries in science. The theory is derived from a recurring theme found in a diverse range of scientific change, scientific discovery, and knowledge diffusion theories…

Generalized topological spaces are not necessarily closed under finite intersections. Moreover, the whole universe does not need to be open. We use modified version of this framework to establish certain models for non-normal modal logics.…

This is a reflection on the author's experience in teaching logic at the graduate level in a computer science department. The main lesson is that model building and the process of modelling must be placed at the centre stage of logic…

There is a wide range of modal logics whose semantics goes beyond relational structures, and instead involves, e.g., probabilities, multi-player games, weights, or neighbourhood structures. Coalgebraic logic serves as a unifying semantic…

Network motifs are often called the building blocks of networks. Analysis of motifs is found to be an indispensable tool for understanding local network structure, in contrast to measures based on node degree distribution and its functions…

Our main result is the equivalence of two notions of reducibility between structures. One is a syntactical notion which is an effective version of interpretability as in model theory, and the other one is a computational notion which is a…

The Kripke semantics of various logics arises via categorical dualities between a category of relational frames and their maps, and a category of algebras and logical homomorphisms. When the relational frames are considered as computational…

We show that strict deterministic propositional dynamic logic with intersection is highly undecidable, solving a problem in the Stanford Encyclopedia of Philosophy. In fact we show something quite a bit stronger. We introduce the…

The internal representations learned by deep networks are often sensitive to architecture-specific choices, raising questions about the stability, alignment, and transferability of learned structure across models. In this paper, we…

In Feferman's work, explicit mathematics and theories of generalized inductive definitions play a central role. One objective of this article is to describe the connections with Martin-Lof type theory and constructive Zermelo-Fraenkel set…

Standpoint linear temporal logic SLTL is a recent formalism able to model possibly conflicting commitments made by distinct agents, taking into account aspects of temporal reasoning. In this paper, we analyse the computational properties of…

Epistemic analysis of distributed systems is one of the biggest successes among applications of logic in computer science. The reason for that is that agents' actions are necessarily guided by their knowledge. Thus, epistemic modal logic,…

Causality is one of the fundamental structures of spacetimes, determining the possible behaviour and propagation of physical information. Causal structure can be analysed through the various modal logics it induces. The modal logics for the…

In this paper, we deal with the problem of putting together modal worlds that operate in different logic systems. When evaluating a modal sentence $\Box \varphi$, we argue that it is not sufficient to inspect the truth of $\varphi$ in…