Related papers: Implicit Kripke Semantics and Ultraproducts in Str…
We deal with the fragment of modal logic consisting of implications of formulas built up from the variables and the constant `true' by conjunction and diamonds only. The weaker language allows one to interpret the diamonds as the uniform…
We discuss the modifications of the Kripke trick simulating binary predicate letters of classical first-order formulas with monadic modal first-order formulas and the situations where the trick does not work. As a result, we obtain results…
We consider the G\"odel bi-modal logic determined by fuzzy Kripke models where both the propositions and the accessibility relation are infinitely valued over the standard G\"odel algebra [0,1] and prove strong completeness of Fischer Servi…
We give a new characterization of elementary and deterministic polynomial time computation in linear logic through the proofs-as-programs correspondence. Girard's seminal results, concerning elementary and light linear logic, achieve this…
As machine learning black boxes are increasingly being deployed in critical domains such as healthcare and criminal justice, there has been a growing emphasis on developing techniques for explaining these black boxes in a post hoc manner.…
We present a Coq formalization of the Quantified Reflection Calculus with one modality, or $\mathsf{QRC}_1$. This is a decidable, strictly positive, and quantified modal logic previously studied for its applications in proof theory. The…
Constraint logic grammars provide a powerful formalism for expressing complex logical descriptions of natural language phenomena in exact terms. Describing some of these phenomena may, however, require some form of graded distinctions which…
In this paper, we propose three novel models to enhance word embedding by implicitly using morphological information. Experiments on word similarity and syntactic analogy show that the implicit models are superior to traditional explicit…
We introduce FIK, a natural intuitionistic modal logic specified by Kripke models satisfying the condition of forward confluence. We give a complete Hilbert-style axiomatization of this logic and propose a bi-nested calculus for it. The…
Simplicial models have become a crucial tool for studying distributed computing. These models, however, are only able to account for the knowledge, but not for the beliefs of agents. We present a new semantics for logics of belief. Our…
A large part of the theory of Hardy spaces on products of Euclidean spaces has been extended to the setting of products of stratified Lie groups. This includes characterisation of Hardy spaces by square functions and by atomic…
Traditionally, formal languages are defined as sets of words. More recently, the alternative coalgebraic or coinductive representation as infinite tries, i.e., prefix trees branching over the alphabet, has been used to obtain compact and…
We propose a uniform method of constructing ultrafilter extensions from canonical models, which is based on the similarity between ultrafilters and maximal consistent sets. This method can help us understand why the known ultrafilter…
We give a new coalgebraic semantics for intuitionistic modal logic with $\Box$. In particular, we provide a colagebraic representation of intuitionistic descriptive modal frames and of intuitonistic modal Kripke frames based on image-finite…
We propose four axiomatic systems for intuitionistic linear temporal logic and show that each of these systems is sound for a class of structures based either on Kripke frames or on dynamic topological systems. Our topological semantics…
We define and study logics in the framework of probabilistic team semantics and over metafinite structures. Our work is paralleled by the recent development of novel axiomatizable and tractable logics in team semantics that are closed under…
Analysis of (partial) groundness is an important application of abstract interpretation. There are several proposals for improving the precision of such an analysis by exploiting type information, icluding our own work with Hill and King,…
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…
Abstract grammatical knowledge - of parts of speech and grammatical patterns - is key to the capacity for linguistic generalization in humans. But how abstract is grammatical knowledge in large language models? In the human literature,…
Multi-modal word semantics aims to enhance embeddings with perceptual input, assuming that human meaning representation is grounded in sensory experience. Most research focuses on evaluation involving direct visual input, however, visual…