Related papers: Topological semantics of conservativity and interp…
Given a structure $M$ we introduce infinitary logic expansions, which generalise the Morleyisation. We show that these expansions are tame, in the sense that they preserve and reflect both the Embedding Ramsey Property (ERP) and the…
While it was defined long ago, the extension of CTL with quantification over atomic propositions has never been studied extensively. Considering two different semantics (depending whether propositional quantification refers to the Kripke…
We look at characterizing which formulas are expressible in rich decidable logics such as guarded fixpoint logic, unary negation fixpoint logic, and guarded negation fixpoint logic. We consider semantic characterizations of definability, as…
Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…
In this paper we show that subsumption problems in lightweight description logics (such as $\mathcal{EL}$ and $\mathcal{EL}^+$) can be expressed as uniform word problems in classes of semilattices with monotone operators. We use…
It is standard to regard the intuitionistic restriction of a classical logic as increasing the expressivity of the logic because the classical logic can be adequately represented in the intuitionistic logic by double-negation, while the…
We carry out a semantic study of the constructive modal logic CK. We provide a categorical duality linking the algebraic and birelational semantics of the logic. We then use this to prove Sahlqvist style correspondence and completeness…
Logical bilateralism challenges traditional concepts of logic by treating assertion and denial as independent yet opposed acts. While initially devised to justify classical logic, its constructive variants show that both acts admit…
We characterize conservative median algebras and semilattices by means of forbidden substructures and by providing their representation as chains. Moreover, using a dual equivalence between median algebras and certain topological…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
We suggest an ordering for the predicates in continuous logic so that the semantics of continuous logic can be formulated as a hyperdoctrine. We show that this hyperdoctrine can be embedded into the hyperdoctrine of subobjects of a suitable…
In this paper, we define an intuitionistic version of Computation Tree Logic. After explaining the semantic features of intuitionistic logic, we examine how these characteristics can be interesting for formal verification purposes.…
We study the problem of fitting ontologies and constraints to positive and negative examples that take the form of a finite relational structure. As ontology and constraint languages, we consider the description logics $\mathcal{E\mkern-2mu…
This paper from 2008 is the first in a series of three related papers on modal methods in interpretability logics and applications. In this first paper the foundations are laid for later results. These foundations consist of a thorough…
Probabilistic systems are an important theme in AI domain. As the specification language, the logic PCTL is now the default logic for reasoning about probabilistic properties. In this paper, we present a natural and succinct probabilistic…
We give an analysis and generalizations of some long-established constructive completeness results in terms of categorical logic and pre-sheaf and sheaf semantics. The purpose is in no small part conceptual and organizational: from a few…
Advances in natural language processing have resulted in increased capabilities with respect to multiple tasks. One of the possible causes of the observed performance gains is the introduction of increasingly sophisticated text…
We explain how to see finite combinatorics of preorders implicit in the {text} of basic topological definitions or arguments in (Bourbaki, General topology, Ch.I), and define a concise combinatorial notation such that complete definitions…
Topological semantics for modal logics has recently gained new momentum in many different branches of logic. In this paper, we will consider the topological semantics of both classical and paraconsistent modal logics. This work is a new…
A prototypical example of categorial grammars are those based on Lambek calculus, i.e. noncommutative intuitionistic linear logic. However, it has been noted that purely noncommutative operations are often not sufficient for modeling even…