Related papers: Topological completeness of the provability logic …
Uncertainty in Logic Programming has been investigated during the last decades, dealing with various extensions of the classical LP paradigm and different applications. Existing proposals rely on different approaches, such as clause…
Goedel's completeness theorem is concerned with provability, while Girard's theorem in ludics (as well as full completeness theorems in game semantics) are concerned with proofs. Our purpose is to look for a connection between these two…
Logics for reasoning about knowledge and actions have seen many applications in various domains of multi-agent systems, including epistemic planning. Change of knowledge based on observations about the surroundings forms a key aspect in…
The topological interpretation of modal logics provides descriptive languages and proof systems for reasoning about points of topological spaces. Recent work has been devoted to model checking of spatial logics on discrete spatial…
There has been renewed interest in recent years in McKinsey and Tarski's interpretation of modal logic in topological spaces and their proof that S4 is the logic of any separable dense-in-itself metric space. Here we extend this work to the…
This paper explores relational syllogistic logics, a family of logical systems related to reasoning about relations in extensions of the classical syllogistic. These are all decidable logical systems. We prove completeness theorems and…
We consider quantified pretransitive Horn modal logic. It is known that such logics are complete with respect to predicate Kripke frames with expanding domains. In this paper we prove that they are also complete with respect to…
A natural topology on the space of left orderings of an arbitrary semi-group is introduced. It is proved that this space is compact and that for free abelian groups it is homeomorphic to the Cantor set. An application of this result is a…
In the recent literature of Artificial Intelligence, an intensive research effort has been spent, for various algebras of qualitative relations used in the representation of temporal and spatial knowledge, on the problem of classifying the…
Plausibility models are Kripke models that agents use to reason about knowledge and belief, both of themselves and of each other. Such models are used to interpret the notions of conditional belief, degrees of belief, and safe belief. The…
This paper presents a bimodal logic for reasoning about knowledge during knowledge acquisition. One of the modalities represents (effort during) non-deterministic time and the other represents knowledge. The semantics of this logic are…
The paper suggests a definition of "know who" as a modality using Grove-Halpern semantics of names. It also introduces a logical system that describes the interplay between modalities "knows who", "knows", and "for all agents". The main…
In this paper we provide a unifying description of different types of semantics of modal logic found in the literature via the framework of topological categories. In the style of categorical logic, we establish an exact correspondence…
This thesis aims to provide a suite of techniques to generate completeness results for coalgebraic logics with axioms of arbitrary rank. We have chosen to investigate the possibility to generalize what is arguably one of the most successful…
We consider a modal logic that can formalise statements about uncertainty and beliefs such as `I think that my wallet is in the drawer rather than elsewhere' or `I am confused whether my appointment is on Monday or Tuesday'. To do that, we…
We explore a fuzzy modal logic that can formalise probabilistic reasoning about actions and knowledge. In particular, we deal with contexts involving statements about events expressed via modal formulas, e.g., "after doing $a$, the…
We show that certain spaces of log-integrable functions and operators are complete topological *-algebras with respect to a natural metric space structure. We explore connections with the Nevanlinna class of holomorphic functions.
This article aims to present a neighborhood semantic for a modal logic, namely, propositional logic of the plausible. As a subnormal character modal logic, not admits a Kripke semantics. However, the authors show that this neighborhood…
This work presents a formalized proof of modal completeness for G\"odel-L\"ob provability logic (GL) in the HOL Light theorem prover. We describe the code we developed, and discuss some details of our implementation, focusing on our choices…
A co-valuation is, essentially, a minimal finite cover. We introduce a logic based on co-valuations, which play the role of valuations of free variables in classical first-order logic, and show that the fundamental tools of model theory --…