We introduce a new formal model -- based on the mathematical construct of sheaves -- for representing contradictory information in textual sources. This model has the advantage of letting us (a) identify the causes of the inconsistency; (b) measure how strong it is; (c) and do something about it, e.g. suggest ways to reconcile inconsistent advice. This model naturally represents the distinction between contradictions and disagreements. It is based on the idea of representing natural language sentences as formulas with parameters sitting on lattices, creating partial orders based on predicates shared by theories, and building sheaves on these partial orders with products of lattices as stalks. Degrees of disagreement are measured by the existence of global and local sections. Limitations of the sheaf approach and connections to recent work in natural language processing, as well as the topics of contextuality in physics, data fusion, topological data analysis and epistemology are also discussed.
Our original motivation in @cite_7 came from modeling medical guidelines, but, as noted above, contradictory sets of documents are pervasive. In the last ten years the field of computational linguistics recognized this phenomenon, and initiated ongoing computational research on reasoning with textual and contradictory information ( @cite_32 , @cite_22 ). The motivation for a new formalization of compatibility comes partially from an opportunity to improve on the methods proposed in @cite_9 .
@cite_9 @cite_22 @cite_32 @cite_7
2739951115 1504212872 176609766 2016630033
We introduce a formal distinction between contradictions and disagreements in natural language texts, motivated by the need to formally reason about contradictory medical guidelines. This is a novel and potentially very useful distinction, and has not been discussed so far in NLP and logic. We also describe a NLP system capable of automated finding contradictory medical guidelines; the system uses a combination of text analysis and information retrieval modules. We also report positive evaluation results on a small corpus of contradictory medical recommendations. Objective : Development of a general natural-language processor that identifies clinical information in narrative reports and maps that information into a structured representation containing clinical terms. @PARASPLIT Design : The natural-language processor provides three phases of processing, all of which are driven by different knowledge sources. The first phase performs the parsing. It identifies the structure of the text through use of a grammar that defines semantic patterns and a target form. The second phase, regularization, standardizes the terms in the initial target structure via a compositional mapping of multi-word phrases. The third phase, encoding, maps the terms to a controlled vocabulary. Radiology is the test domain for the processor and the target structure is a formal model for representing clinical information in that domain. @PARASPLIT Measurements : The impression sections of 230 radiology reports were encoded by the processor. Results of an automated query of the resultant database for the occurrences of four diseases were compared with the analysis of a panel of three physicians to determine recall and precision. @PARASPLIT Results : Without training specific to the four diseases, recall and precision of the system(combined effect of the processor and query generator) were 70 and 87 . Training of the query component increased recall to 85 without changing precision. Horn clause logic programming can be extended to include abduction with integrity constraints. In the resulting extension of logic programming, negation by failure can be simulated by making negative conditions abducible and by imposing appropriate denials and disjunctions as integrity constraints. This gives an alternative semantics for negation by failure, which generalises the stable model semantics of negation by failure. The abductive extension of logic programming extends negation by failure in three ways: (1) computation can be perfonned in alternative minimal models, (2) positive as well as negative conditions can be made abducible, and (3) other integrity constraints can also be accommodated. * This paper was written while the first author was at Imperial College. 235 Introduction The tenn "abduction" was introduced by the philosopher Charles Peirce [1931] to refer to a particular kind of hypothetical reasoning. In the simplest case, it has the fonn: From A and A fB infer B as a possible "explanation" of A. Abduction has been given prominence in Charniak and McDennot's [1985] "Introduction to Artificial Intelligence", where it has been applied to expert systems and story comprehension. Independently, several authors have developed deductive techniques to drive the generation of abductive hypotheses. Cox and Pietrzykowski [1986] construct hypotheses from the "dead ends" of linear resolution proofs. Finger and Genesereth [1985] generate "deductive solutions to design problems" using the "residue" left behind in resolution proofs. Poole, Goebel and Aleliunas [1987] also use linear resolution to generate hypotheses. All impose the restriction that hypotheses should be consistent with the "knowledge base". Abduction is a fonn of non-monotonic reasoning, because hypotheses which are consistent with one state of a knowledge base may become inconSistent when new knowledge is added. Poole [1988] argues that abduction is preferable to noh-monotonic logics for default reasoning. In this view, defaults are hypotheses fonnulated within classical logic rather than conclusions derived withln some fonn of non-monotonic logic. The similarity between abduction and default reasoning was also pointed out in [Kowalski, 1979]. In this paper we show how abduction can be integrated with logic programming, and we concentrate on the use of abduction to generalise negation by failure. Conditional Answers Compared with Abduction In the simplest case, a logic program consists of a set of Horn Clauses, which are used backward to_reduce goals to sub goals. The initial goal is solved when there are no subgollls left; This paper describes a system and set of algorithms for automatically inducing stand-alone monolingual part-of-speech taggers, base noun-phrase bracketers, named-entity taggers and morphological analyzers for an arbitrary foreign language. Case studies include French, Chinese, Czech and Spanish.Existing text analysis tools for English are applied to bilingual text corpora and their output projected onto the second language via statistically derived word alignments. Simple direct annotation projection is quite noisy, however, even with optimal alignments. Thus this paper presents noise-robust tagger, bracketer and lemmatizer training procedures capable of accurate system bootstrapping from noisy and incomplete initial projections.Performance of the induced stand-alone part-of-speech tagger applied to French achieves 96 core part-of-speech (POS) tag accuracy, and the corresponding induced noun-phrase bracketer exceeds 91 F-measure. The induced morphological analyzer achieves over 99 lemmatization accuracy on the complete French verbal system.This achievement is particularly noteworthy in that it required absolutely no hand-annotated training data in the given language, and virtually no language-specific knowledge or resources beyond raw text. Performance also significantly exceeds that obtained by direct annotation projection.