Related papers: Product closure of some second-order modal logics
Generalizing standard monadic second-order logic for Kripke models, we introduce monadic second-order logic interpreted over coalgebras for an arbitrary set functor. We then consider invariance under behavioral equivalence of MSO-formulas.…
We introduce a framework for reasoning about the security of computer systems using modal logic. This framework is sufficiently expressive to capture a variety of known security properties, while also being intuitive and independent of…
An exhaustive survey of categorical propositions is proposed in the present paper, both with respect to their nature and the logical problems raised by them. Through a comparative analysis of Term Logic and First-Order Logic, it is shown…
Standpoint extensions of knowledge representation formalisms have been recently introduced as a means to incorporate multi-perspective modelling and reasoning through modal operators that attribute pieces of knowledge to specific entities…
In this paper, we revisit Moggi's celebrated calculus of computational effects from the perspective of logic of monoidal action (actegory). Our development takes the following steps. Firstly, we perform proof-theoretic reconstruction of…
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…
Functional logic languages are a high-level approach to programming by combining the most important declarative features. They abstract from small-step operational details so that programmers can concentrate on the logical aspects of an…
In this paper we introduce a simple modal logic framework to reason about the expertise of an information source. In the framework, a source is an expert on a proposition $p$ if they are able to correctly determine the truth value of $p$ in…
The first-order theory of MALL (multiplicative, additive linear logic) over only equalities is an interesting but weak logic since it cannot capture unbounded (infinite) behavior. Instead of accounting for unbounded behavior via the…
This paper presents a two-dimensional modal logic for reasoning about the changing patterns of knowledge and social relationships in networks organised on the basis of a symmetric 'friendship' relation, providing a precise language for…
To formalize patterns of information increase and decrease, Van Benthem (1996) proposed modal information logic (MIL), a modal logic over partial orders. In MIL, points are interpreted as information states and least upper bounds, when…
The formal construction of the second-order logic or predicate calculus essentially adds quantifiers to propositional logic. Why second-order logic cannot be reduced to that of the first order? How to demonstrate that certain predicates are…
Open bisimilarity is defined for open process terms in which free variables may appear. The insight is, in order to characterise open bisimilarity, we move to the setting of intuitionistic modal logics. The intuitionistic modal logic…
We introduce the abstract notions of "monadic operational semantics", a small-step semantics where computational effects are modularly modeled by a monad, and "type-and-effect system", including "effect types" whose interpretation lifts…
A shallow semantical embedding for public announcement logic with relativized common knowledge is presented. This embedding enables the first-time automation of this logic with off-the-shelf theorem provers for classical higher-order logic.…
As historically acknowledged in the Reasoning about Actions and Change community, intuitiveness of a logical domain description cannot be fully automated. Moreover, like any other logical theory, action theories may also evolve, and thus…
The Distributed Ontology Language (DOL) is currently being standardized within the OntoIOp (Ontology Integration and Interoperability) activity of ISO/TC 37/SC 3. It aims at providing a unified framework for (1) ontologies formalized in…
We introduce a novel decidable fragment of first-order logic. The fragment is one-dimensional in the sense that quantification is limited to applications of blocks of existential (universal) quantifiers such that at most one variable…
Model editing has become an increasingly popular alternative for efficiently updating knowledge within language models. Current methods mainly focus on reliability, generalization, and locality, with many methods excelling across these…
View update is an important mechanism that allows updates on a view by translating them into the corresponding updates on the base relations. The existing literature has shown the ambiguity of translating view updates. To address this…