Linguistic quantifiers modeled by Sugeno integrals

Since quantifiers have the ability of summarizing the properties of a class of objects without enumerating them, linguistic quantification is a very important topic in the field of high level knowledge representation and reasoning. This paper introduces a new framework for modeling quantifiers in natural languages in which each linguistic quantifier is represented by a family of fuzzy measures, and the truth value of a quantified proposition is evaluated by using Sugeno's integral. This framework allows us to have some elegant logical properties of linguistic quantifiers. We compare carefully our new model of quantification and other approaches to linguistic quantifiers. A set of criteria for linguistic quantification was proposed in the previous literature. The relationship between these criteria and the results obtained in the present paper is clarified. Some simple applications of the Sugeno's integral semantics of quantifiers are presented. © 2006 Elsevier B.V. All rights reserved

A Fuzzy Syllogistic Reasoning Schema for Generalized Quantifiers

In this paper, a new approximate syllogistic reasoning schema is described that expands some of the approaches expounded in the literature into two ways: (i) a number of different types of quantifiers (logical, absolute, proportional, comparative and exception) taken from Theory of Generalized Quantifiers and similarity quantifiers, taken from statistics, are considered and (ii) any number of premises can be taken into account within the reasoning process. Furthermore, a systematic reasoning procedure to solve the syllogism is also proposed, interpreting it as an equivalent mathematical optimization problem, where the premises constitute the constraints of the searching space for the quantifier in the conclusion.Comment: 22 pages, 6 figures, journal pape

Bayesian Inference Semantics: A Modelling System and A Test Suite

We present BIS, a Bayesian Inference Seman- tics, for probabilistic reasoning in natural lan- guage. The current system is based on the framework of Bernardy et al. (2018), but de- parts from it in important respects. BIS makes use of Bayesian learning for inferring a hy- pothesis from premises. This involves estimat- ing the probability of the hypothesis, given the data supplied by the premises of an argument. It uses a syntactic parser to generate typed syn- tactic structures that serve as input to a model generation system. Sentences are interpreted compositionally to probabilistic programs, and the corresponding truth values are estimated using sampling methods. BIS successfully deals with various probabilistic semantic phe- nomena, including frequency adverbs, gener- alised quantifiers, generics, and vague predi- cates. It performs well on a number of interest- ing probabilistic reasoning tasks. It also sus- tains most classically valid inferences (instan- tiation, de Morgan’s laws, etc.). To test BIS we have built an experimental test suite with examples of a range of probabilistic and clas- sical inference patterns