Related papers: Modal Matters in Interpretability Logics
The social and implicit nature of human communication ramifies readers' understandings of written sentences. Single gold-standard interpretations rarely exist, challenging conventional assumptions in natural language processing. This work…
The study of modal logic has witnessed tremendous development following the introduction of Kripke semantics. However, recent developments in programming languages and type theory have led to a second way of studying modalities, namely…
Mechanistic interpretability aims to explain neural model behaviour by reverse-engineering learned computational structure into human-understandable components. Without a formal framework, however, mechanistic explanations cannot be…
Recently, much work has been carried out to study simplicial interpretations of modal logic. While notions of (distributed) knowledge have been well investigated in this context, it has been open how to model belief in simplicial models. We…
Non-additive uncertainty theories, typically possibility theory, belief functions and imprecise probabilities share a common feature with modal logic: the duality properties between possibility and necessity measures, belief and…
Most existing evaluations of explainable machine learning (ML) methods rely on simplifying assumptions or proxies that do not reflect real-world use cases; the handful of more robust evaluations on real-world settings have shortcomings in…
This paper is aimed at providing a uniform framework for reasoning about beliefs of multiple agents and their fusion. In the first part of the paper, we develop logics for reasoning about cautiously merged beliefs of agents with different…
The use of formal language for deductive logical reasoning aligns well with language models (LMs), where translating natural language (NL) into first-order logic (FOL) and employing an external solver results in a verifiable and therefore…
The G\"odel translation provides an embedding of the intuitionistic logic $\mathsf{IPC}$ into the modal logic $\mathsf{Grz}$, which then embeds into the modal logic $\mathsf{GL}$ via the splitting translation. Combined with Solovay's…
Large Language Models (LLMs) are becoming increasingly popular in pervasive computing due to their versatility and strong performance. However, despite their ubiquitous use, the exact mechanisms underlying their outstanding performance…
A simple framework for reasoning under uncertainty and intervention is introduced. This is achieved in three steps. First, logic is restated in set-theoretic terms to obtain a framework for reasoning under certainty. Second, this framework…
In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The…
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…
Cathoristic logic is a multi-modal logic where negation is replaced by a novel operator allowing the expression of incompatible sentences. We present the syntax and semantics of the logic including complete proof rules, and establish a…
We initiate the study of finite characterizations and exact learnability of modal languages. A finite characterization of a modal formula w.r.t. a set of formulas is a finite set of finite models (labelled either positive or negative) which…
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…
We propose a new modal logic endowed with a simple deductive system to interpret Aristotle's theory of the modal syllogism. While being inspired by standard propositional modal logic it is also a logic of terms that admits a (sound)…
This paper is about the computability of the modal definability problem in classes of frames determined by Euclidean modal logics. We characterize those Euclidean modal logics such that the classes of frames they determine give rise to an…
Autonomous agents are supposed to be able to finish tasks or achieve goals that are assigned by their users through performing a sequence of actions. Since there might exist multiple plans that an agent can follow and each plan might…
It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…