Related papers: Arrow-Type Impossibility for Genuinely Modal Judgm…
In this paper we investigate the complexity of abduction, a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining the world's behavior it aims at finding an explanation for some observed manifestation.…
Autoregressive (AR) language models enforce a fixed left-to-right generation order, creating a fundamental limitation when the required output structure conflicts with natural reasoning (e.g., producing answers before explanations due to…
We study the modal logic of the closure algebra $P_2$, generated by the set of all polygons in the Euclidean plane $\mathbb{R}^2$. We show that this logic is finitely axiomatizable, is complete with respect to the class of frames we call…
Despite a sea of interpretability methods that can produce plausible explanations, the field has also empirically seen many failure cases of such methods. In light of these results, it remains unclear for practitioners how to use these…
For each natural number $n$ we study the modal logic determined by the class of transitive Kripke frames in which there are no cycles of length greater than $n$ and no strictly ascending chains. The case $n=0$ is the G\"odel-L\"ob…
Despite a growing literature on explaining neural networks, no consensus has been reached on how to explain a neural network decision or how to evaluate an explanation. Our contributions in this paper are twofold. First, we investigate…
This work builds upon a well-established research tradition on modal logics of awareness. One of its aims is to export tools and techniques to other areas within modal logic. To this end, we illustrate a number of significant bridges with…
Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…
Large Language Models (LLMs), despite achieving state-of-the-art results in a number of evaluation tasks, struggle to maintain their performance when logical reasoning is strictly required to correctly infer a prediction. In this work, we…
We establish a novel connection between two research areas in non-classical logics which have been developed independently of each other so far: on the one hand, input/output logic, introduced within a research program developing logical…
In this paper, we deal with the problem of putting together modal worlds that operate in different logic systems. When evaluating a modal sentence $\Box \varphi$, we argue that it is not sufficient to inspect the truth of $\varphi$ in…
This article explicitly constructs and classifies all arrovian voting systems on three or more alternatives. If we demand orderings to be complete, we have, of course, Arrow's classical dictator theorem, and a closer look reveals the…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
We extend the logical categories framework to first order modal logic. In our modal categories, modal operators are applied directly to subobjects and interact with the background factorization system. We prove a Joyal-style representation…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
In the context of general rough sets, the act of combining two things to form another is not straightforward. The situation is similar for other theories that concern uncertainty and vagueness. Such acts can be endowed with additional…
Given a logic presented in a sequent calculus, a natural question is that of equivalence of proofs: to determine whether two given proofs are equated by any denotational semantics, ie any categorical interpretation of the logic compatible…
In many contexts the modal properties of a structure change, either due to the impact of a changing environment, fatigue, or due to the presence of structural damage. For example during flight, an aircraft's modal properties are known to…
Gradual semantics within abstract argumentation associate a numeric score with every argument in a system, which represents the level of acceptability of this argument, and from which a preference ordering over arguments can be derived.…
It is shown that, since an ultrafilter over an operator-algebraically finite (i.e. isomorphic to the lattice of projectors of a finite Von Neumann algebra) quantum logic is not necessarily principal, Arrow's Impossibility Theorem doesn't…