Paraconsistency and Word Puzzles

TL;DR

This paper introduces a paraconsistent logic framework using Annotated Predicate Calculus with a new semantics to handle inconsistent information in word puzzles and natural language representations, enhancing robustness and interpretability.

Contribution

It proposes a novel non-monotonic semantics for APC called consistency preferred stable models, enabling effective reasoning with inconsistent data in natural language processing.

Findings

APC with the new semantics effectively manages inconsistencies in word puzzles.

The approach can be integrated into existing CNL translators like ACE and PENG Light.

APC with preferences can be embedded in ASP and implemented in Clingo with Asprin.

Abstract

Word puzzles and the problem of their representations in logic languages have received considerable attention in the last decade (Ponnuru et al. 2004; Shapiro 2011; Baral and Dzifcak 2012; Schwitter 2013). Of special interest is the problem of generating such representations directly from natural language (NL) or controlled natural language (CNL). An interesting variation of this problem, and to the best of our knowledge, scarcely explored variation in this context, is when the input information is inconsistent. In such situations, the existing encodings of word puzzles produce inconsistent representations and break down. In this paper, we bring the well-known type of paraconsistent logics, called Annotated Predicate Calculus (APC) (Kifer and Lozinskii 1992), to bear on the problem. We introduce a new kind of non-monotonic semantics for APC, called consistency preferred stable models and argue that it makes APC into a suitable platform for dealing with inconsistency in word puzzles and, more generally, in NL sentences. We also devise a number of general principles to help the user choose among the different representations of NL sentences, which might seem equivalent but, in fact, behave differently when inconsistent information is taken into account. These principles can be incorporated into existing CNL translators, such as Attempto Controlled English (ACE) (Fuchs et al. 2008) and PENG Light (White and Schwitter 2009). Finally, we show that APC with the consistency preferred stable model semantics can be equivalently embedded in ASP with preferences over stable models, and we use this embedding to implement this version of APC in Clingo (Gebser et al. 2011) and its Asprin add-on (Brewka et al. 2015).