We show that LLMs hallucinate because their output is not constrained to be synonymous with claims for which they have evidence: a condition that we call evidential closure. Information about the truth or falsity of sentences is not statistically identified in the standard neural probabilistic language model setup, and so cannot be conditioned on to generate new strings. We then show how to constrain LLMs to produce output that does satisfy evidential closure. A multimodal LLM must learn about the external world (perceptual learning); it must learn a mapping from strings to states of the world (extensional learning); and, to achieve fluency when generalizing beyond a body of evidence, it must learn mappings from strings to their synonyms (intensional learning). The output of a unimodal LLM must be synonymous with strings in a validated evidence set. Finally, we present a heuristic procedure, Learn-Babble-Prune, that yields faithful output from an LLM by rejecting output that is not synonymous with claims for which the LLM has evidence.

In this paper, we propose a variant of Answer Set Programming (ASP) with evaluable functions that extends their application to sets of objects, something that allows a fully logical treatment of aggregates. Formally, we start from the syntax of First Order Logic with equality and the semantics of Quantified Equilibrium Logic with evaluable functions (QELF). Then, we proceed to incorporate a new kind of logical term, intensional set (a construct commonly used to denote the set of objects characterised by a given formula), and to extend QELF semantics for this new type of expression. In our extended approach, intensional sets can be arbitrarily used as predicate or function arguments or even nested inside other intensional sets, just as regular first-order logical terms. As a result, aggregates can be naturally formed by the application of some evaluable function (count, sum, maximum, etc) to a set of objects expressed as an intensional set. This approach has several advantages. First, while other semantics for aggregates depend on some syntactic transformation (either via a reduct or a formula translation), the QELF interpretation treats them as regular evaluable functions, providing a compositional semantics and avoiding any kind of syntactic restriction. Second, aggregates can be explicitly defined now within the logical language by the simple addition of formulas that fix their meaning in terms of multiple applications of some (commutative and associative) binary operation. For instance, we can use recursive rules to define sum in terms of integer addition. Last, but not least, we prove that the semantics we obtain for aggregates coincides with the one defined by Gelfond and Zhang for the Alog language, when we restrict to that syntactic fragment. (Under consideration for acceptance in TPLP)

This article presents some fundamental ideas about representing knowledge and dealing with meaning in computer representations. I will describe the issues as I currently understand them and describe how they came about, how they fit together, what problems they solve, and some of the things that the resulting framework can do. The ideas apply not just to graph-structured "node-and-link" representations, sometimes called semantic networks, but also to representations referred to variously as frames with slots, entities with relationships, objects with attributes, tables with columns, and records with fields and to the classes and variables of object-oriented data structures. I will start by describing some background experiences and thoughts that preceded the writing of my 1975 paper, "What's in a Link," which introduced many of these issues. After that, I will present some of the key ideas from that paper with a discussion of how some of those ideas have matured since then.

The need of handling semantic heterogeneity of resources is a key problem of the Semantic Web. State of the art techniques for ontology matching are the key technology for addressing this issue. However, they only partially exploit the natural lan- guage descriptions of ontology entities and they are mostly unable to find correspondences between entities having dif- ferent logical types (e.g. mapping properties to classes). We introduce a novel approach aimed at finding correspondences between ontology entities according to the intensional mean- ing of their models, hence abstracting from their logical types. Lexical linked open data and frame semantics play a crucial role in this proposal. We argue that this approach may lead to a step ahead in the state of the art of ontology matching, and positively affect related applications such as question an- swering and knowledge reconciliation.

The ViewGen model of belief ascription assumes that each agent involved in a conversation has a belief space which includes models of what other parties to the conversation believe. The distinctive notion is that a basic procedure, called belief ascription, allows belief spaces to be amalgamated so as to model the updating and augmentation of belief environments. In this paper we extend the ViewGen model to a more general account of reference phenomena, in particular by the notion of a reachable ascription set (RAS) that links intensional objects across belief environments so as to locate the most heuristically plausible referent at a given point in a conversation. The key notion is the location and attachment of entities that may be under different descriptions, the consequent updating of the system's beliefs about other agents by default, and the role in that process of a speaker's and hearer's protocols that ensure that the choice is the appropriate one. An important characteristic of this model is that each communicator considers nothing beyond his own belief space. A conclusion we shall draw is that traditional binary distinctions in this area (like de dicto/de re and attributive/referential) neither classify the examples effectively nor do they assist in locating referents, whereas the single procedure we suggest does both. We also suggest ways in which this analysis can also illuminate other traditional distinctions such as referential and attributive use. The description here is not on an implemented system with results but a theoretical tool to be implemented within an established dialogue platform (such as Wilks et al. 2011).