Related papers: Lattice-Based Graded Logic: a Multimodal Approach

Choice constructs are an important part of the language of logic programming, yet the study of their semantics has been a challenging task. So far, only two-valued semantics have been studied, and the different proposals for such semantics…

The aim of illocutionary logic is to explain how context can affect the meaning of certain special kinds of performative utterances. Recall that performative utterances are understood as follows: a speaker performs the illocutionary act…

We introduce proper display calculi for basic monotonic modal logic, the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…

We claim that LLMs can be paired with formal analysis methods to provide accessible, relevant feedback for HRI tasks. While logic specifications are useful for defining and assessing a task, these representations are not easily interpreted…

Semantic data and knowledge infrastructures must reconcile two fundamentally different forms of representation: natural language, in which most knowledge is created and communicated, and formal semantic models, which enable…

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…

We start from two closure operators defined on the elements of a special kind of partially ordered sets, called causal nets. Causal nets are used to model histories of concurrent processes, recording occurrences of local states and of…

This paper argues that a combined treatment of probabilities, time and actions is essential for an appropriate logical account of the notion of probability; and, based on this intuition, describes an expressive probabilistic temporal logic…

Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more…

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…

Quantitative characterizations and estimations of uncertainty are of fundamental importance in optimization and decision-making processes. Herein, we propose intuitive scores, which we call certainty and doubt, that can be used in both a…

Multimodal semantic understanding often has to deal with uncertainty, which means the obtained messages tend to refer to multiple targets. Such uncertainty is problematic for our interpretation, including inter- and intra-modal uncertainty.…

The ability to accurately interpret implied meanings plays a crucial role in human communication and language use, and language models are also expected to possess this capability. This study demonstrates that providing language models with…

Counting propositional logic was recently introduced in relation to randomized computation and shown able to logically characterize the full counting hierarchy. In this paper we aim to clarify the intuitive meaning and expressive power of…

We extend the meet-implication fragment of propositional intuitionistic logic with a meet-preserving modality. We give semantics based on semilattices and a duality result with a suitable notion of descriptive frame. As a consequence we…

Multi-round incomplete information tasks are crucial for evaluating the lateral thinking capabilities of large language models (LLMs). Currently, research primarily relies on multiple benchmarks and automated evaluation metrics to assess…

We examine four approaches for dealing with the logical omniscience problem and their potential applicability: the syntactic approach, awareness, algorithmic knowledge, and impossible possible worlds. Although in some settings these…

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…

The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…

Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…