Related papers: Ultrafilter Extensions for Veltman Semantics
This paper presents an operational semantics for UML activity diagrams. The purpose of this semantics is three-fold: to give a robust basis for verifying model correctness; to help validate model transformations; and to provide a…
Structures based on polarities have been used to provide relational semantics for propositional logics that are modelled algebraically by non-distributive lattices with additional operators. This article develops a first order notion of…
Using a recently introduced algebraic framework for the classification of fragments of first-order logic, we study the complexity of the satisfiability problem for several ordered fragments of first-order logic, which are obtained from the…
We propose a formalism for representation of finite languages, referred to as the class of IDL-expressions, which combines concepts that were only considered in isolation in existing formalisms. The suggested applications are in natural…
We develop team semantics for Linear Temporal Logic (LTL) to express hyperproperties, which have recently been identified as a key concept in the verification of information flow properties. Conceptually, we consider an asynchronous and a…
We show that the vast majority of extensions of the description logic $\mathcal{EL}$ do not enjoy the Craig interpolation nor the projective Beth definability property. This is the case, for example, for $\mathcal{EL}$ with nominals,…
With the advent of larger and more complex deep learning models, such as in Natural Language Processing (NLP), model qualities like explainability and interpretability, albeit highly desirable, are becoming harder challenges to tackle and…
This paper develops the model theory of normal modal logics based on partial "possibilities" instead of total "worlds," following Humberstone (1981) instead of Kripke (1963). Possibility semantics can be seen as extending to modal logic the…
We argue that existing definitions of interpretability are not actionable in that they fail to inform users about general, sound, and robust interpretable model design. This makes current interpretability research fundamentally ill-posed.…
Unlike classical lexical overlap metrics such as BLEU, most current evaluation metrics for machine translation (for example, COMET or BERTScore) are based on black-box large language models. They often achieve strong correlations with human…
Logics of limited belief aim at enabling computationally feasible reasoning in highly expressive representation languages. These languages are often dialects of first-order logic with a weaker form of logical entailment that keeps reasoning…
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…
As machine learning becomes more widespread and is used in more critical applications, it's important to provide explanations for these models, to prevent unintended behavior. Unfortunately, many current interpretability methods struggle…
An approach to universal (meta-)logical reasoning in classical higher-order logic is employed to explore and study simplifications of Kurt G\"odel's modal ontological argument. Some argument premises are modified, others are dropped, modal…
Given an ordered structure, we study a natural way to extend the order to preorders on type spaces. For definably complete, linearly ordered structures, we give a characterisation of the preorder on the space of 1-types. We apply these…
The famous van Benthem theorem states that modal logic corresponds exactly to the fragment of first-order logic that is invariant under bisimulation. In this article we prove an exact analogue of this theorem in the framework of modal…
Large language models (LLMs) have demonstrated impressive capabilities in natural language processing. However, their internal mechanisms are still unclear and this lack of transparency poses unwanted risks for downstream applications.…
Separation logic is a concise method for specifying programs that manipulate dynamically allocated storage. Partially inspired by separation logic, Implicit Dynamic Frames has recently been proposed, aiming at first-order tool support. In…
We introduce the first order logic of proofs $FOLP^\Box$ in the joint language combining justification terms and binding modalities. The main issue is Kripke--style semantics for this logic. We describe models for $FOLP^\Box$ in terms of…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…