相关论文: A non-uniform view of Craig interpolation in modal…
We combine the concepts of modal logics and many-valued logics in a general and comprehensive way. Namely, given any finite linearly ordered set of truth values and any set of propositional connectives defined by truth tables, we define the…
The paper considers algorithmic properties of classical and non-classical first-order logics and theories in bounded languages. The main idea is to prove the undecidability of various fragments of classical and non-classical first-order…
This chapter presents a state-of-the-art survey of relationships, traditionally referred to as `bridges', between interpolation properties for propositional logics -- including superintuitionistic, modal, and substructural logics -- and…
Non-iterative normal modal logics are defined by axioms of modal degree 1. In this paper we use calculations with normal forms to determine the set of all possible non-iterative normal modal logics, unimodal propositional extensions of K.…
We present new descriptive complexity characterisations of classes REG (regular languages), LCFL (linear context-free languages) and CFL (context-free languages) as restrictions on inference rules, size of formulae and permitted connectives…
Inquisitive modal logic, InqML, is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that…
As part of a broader family of logics, [1, 3] introduced two key logical systems: $\mathsf{iK_{d}}$, which encapsulates the basic logical structure of dynamic topological systems, and $\mathsf{iK_{d*}}$, which provides a well-behaved yet…
There are exactly two maximal schematic extensions of the relevant logic R with the variable sharing property. We establish that one of them has a strong form of interpolation for deducibility, thereby giving an example of a well-known…
It was recently shown that the theory of linear stochastic systems can be viewed as a particular case of the theory of linear systems on a certain commutative ring of power series in a countable number of variables. In the present work we…
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…
We prove analogues of the Craig interpolation theorem for the continuous model theory of metric structures.
We prove that a three-dimensional smooth complete intersection of two quadrics over a field k is k-rational if and only if it contains a line defined over k. To do so, we develop a theory of intermediate Jacobians for geometrically rational…
On relational structures and on polymodal logics, we describe operations which preserve local tabularity. This provides new sufficient semantic and axiomatic conditions for local tabularity of a modal logic. The main results are the…
We consider existential rules (aka Datalog+) as a formalism for specifying ontologies. In recent years, many classes of existential rules have been exhibited for which conjunctive query (CQ) entailment is decidable. However, most of these…
We describe a new method of finding interpolants for classical logic using certain refutation system as a starting point. Refutation can be thought of as an alternative approach to the analysis of formal systems: instead of focusing on…
We prove the uniform Lyndon interpolation property (ULIP) of some extensions of the pure logic of necessitation $\mathbf{N}$. For any $m, n \in \mathbb{N}$, $\mathbf{N}^+\mathbf{A}_{m,n}$ is the logic obtained from $\mathbf{N}$ by adding a…
In this work we study the decidability of a class of global modal logics arising from Kripke frames evaluated over certain residuated lattices, known in the literature as modal many-valued logics. We exhibit a large family of these modal…
The relationship between interpolation and separation properties of hypersurfaces in Bargmann-Fock spaces over $\mathbb{C} ^n$ is not well-understood except for $n=1$. We present four examples of smooth affine algebraic hypersurfaces that…
Graded modal logic is the formal language obtained from ordinary (propositional) modal logic by endowing its modal operators with cardinality constraints. Under the familiar possible-worlds semantics, these augmented modal operators receive…
We present a novel investigation into the consistency operator ($\circ$), traditionally associated with paraconsistent logics, as a means of capturing non-normal modal classicalities within the Kripke framework. By semantically…