Related papers: Lattice-Based Graded Logic: a Multimodal Approach
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…
We propose a formalization of the three-tier causal hierarchy of association, intervention, and counterfactuals as a series of probabilistic logical languages. Our languages are of strictly increasing expressivity, the first capable of…
Probabilistic puzzles can be confusing, partly because they are formulated in natural languages - full of unclarities and ambiguities - and partly because there is no widely accepted and intuitive formal language to express them. We propose…
The forensic science community has increasingly sought quantitative methods for conveying the weight of evidence. Experts from many forensic laboratories summarize their findings in terms of a likelihood ratio. Several proponents of this…
This paper argues for a modal view of probability. The syntax and semantics of one particularly strong probability logic are discussed and some examples of the use of the logic are provided. We show that it is both natural and useful to…
By using the abstract structures investigated in the first Part of this article, we develop a semantics for an epistemic language, which expresses sentences like "Alice knows that Bob does not understand that PI is irrational". One is…
Applying automated reasoning tools for decision support and analysis in law has the potential to make court decisions more transparent and objective. Since there is often uncertainty about the accuracy and relevance of evidence,…
We describe a notion of categorical model for unitless fragments of (multiplicative) linear logic. The basic definition uses promonoidal categories, and we also give an equivalent elementary axiomatisation.
We consider a simple modal logic whose non-modal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of…
In this paper an approach to automated deduction under uncertainty,based on possibilistic logic, is proposed ; for that purpose we deal with clauses weighted by a degree which is a lower bound of a necessity or a possibility measure,…
The Galois lattice is a graphic method of representing knowledge structures. The first basic purpose in this paper is to introduce a new class of Galois lattices, called graded Galois lattices. As a direct result, one can obtain the notion…
In this article, we add a diamond to the parametrized box-based propositional language of intuitionistic doxastic logic and intuitionistic epistemic logic introduced by Artemov and Protopopescu. The main results of this article are the…
This chapter presents probability logic as a rationality framework for human reasoning under uncertainty. Selected formal-normative aspects of probability logic are discussed in the light of experimental evidence. Specifically, probability…
We show how categorial deduction can be implemented in higher-order (linear) logic programming, thereby realising parsing as deduction for the associative and non-associative Lambek calculi. This provides a method of solution to the parsing…
We propose a general framework to allow: (a) specifying the operational semantics of a programming language; and (b) stating and proving properties about program correctness. Our framework is based on a many-sorted system of hybrid modal…
Large language models perform well on many logical reasoning benchmarks, but it remains unclear which core logical skills they truly master. To address this, we introduce LogicSkills, a benchmark that isolates three fundamental logical…
We present machine-learning-based approaches for determining the \emph{degree} of inconsistency -- which is a numerical value -- for propositional logic knowledge bases. Specifically, we present regression- and neural-based models that…
Gradual semantics (GS) have demonstrated great potential in argumentation, in particular for deploying quantitative bipolar argumentation frameworks (QBAFs) in a number of real-world settings, from judgmental forecasting to explainable AI.…
Large language models (LLMs) are stochastic, and not all models give deterministic answers, even when setting temperature to zero with a fixed random seed. However, few benchmark studies attempt to quantify uncertainty, partly due to the…
Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…