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We look at equivalence relations on the set of models of a theory -- MERs, for short -- such that the class of equivalent pairs is itself an elementary class, in a language appropriate for pairs of models. We provide many examples of…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…
When making simultaneous decisions, our preference for the outcomes on one subset can depend on the outcomes on a disjoint subset. In referendum elections, this gives rise to the separability problem, where a voter must predict the outcome…
Large language models (LLMs) are increasingly used in domains where causal reasoning matters, yet it remains unclear whether their judgments reflect normative causal computation, human-like shortcuts, or brittle pattern matching. We…
The purpose of this paper is to introduce justification logics based on conditional logics. We introduce a new family of logics, called conditional justification logics, which incorporates a counterfactual conditional in its language. For…
Logical relations built on top of an operational semantics are one of the most successful proof methods in programming language semantics. In recent years, more and more expressive notions of operationally-based logical relations have been…
This article contributes to the debate of the meaning of relationalism and background independence, which has remained of interest in theoretical physics from Newton versus Leibniz through to foundational issues for today's leading…
When we work with information from multiple sources, the formalism each employs to handle uncertainty may not be uniform. In order to be able to combine these knowledge bases of different formats, we need to first establish a common basis…
Recent published work has addressed the Shalqvist correspondence problem for non-distributive logics. The natural question that arises is to identify the fragment of first-order logic that corresponds to logics without distribution, lifting…
We introduce a family of comparative plausibility logics over neighbourhood models, generalising Lewis' comparative plausibility operator over sphere models. We provide axiom systems for the logics, and prove their soundness and…
Given a consequence relation in many-valued logic, what connectives can be defined? For instance, does there always exist a conditional operator internalizing the consequence relation, and which form should it take? In this paper, we pose…
We study probabilistic team semantics which is a semantical framework allowing the study of logical and probabilistic dependencies simultaneously. We examine and classify the expressive power of logical formalisms arising by different…
LP$^{\supset,\mathsf{F}}$ is a three-valued paraconsistent propositional logic which is essentially the same as J3. It has most properties that have been proposed as desirable properties of a reasonable paraconsistent propositional logic.…
Large language models (LLMs) has been widely adopted as a scalable surrogate for human evaluation, yet such judges remain imperfect and susceptible to surface-level biases. One possible reason is that these judges lack sufficient…
Matching logic is a general formal framework for reasoning about a wide range of theories, with particular emphasis on programming language semantics. Notably, the intermediate language of the K semantics framework is an extension of…
The article describes the structural and algorithmic relations between Cartesian trees and Lyndon Trees. This leads to a uniform presentation of the Lyndon table of a word corresponding to the Next Nearest Smaller table of a sequence of…
The classical decision problem, as it is understood today, is the quest for a delineation between the decidable and the undecidable parts of first-order logic based on elegant syntactic criteria. In this paper, we treat the concept of…
Contextuality and nonlocality are non-classical properties exhibited by quantum statistics whose implications profoundly impact both foundations and applications of quantum theory. In this paper we provide some insights into logical…
We analyze a few illustrative examples of scenarios in which relativistic symmetries are deformed by Planck-scale effects in particle-type-dependent manner. The novel mathematical structures required by such scenarios are the mixing…
We give a novel approach to proving soundness and completeness for a logic (henceforth: the object-logic) that bypasses truth-in-a-model to work directly with validity. Instead of working with specific worlds in specific models, we reason…