A Monotonicity Calculus and Its Completeness

Icard, Thomas; Moss, Lawrence S.; Tune, William

doi:10.18653/v1/w17-3408

Cited by 9 publications

(11 citation statements)

References 19 publications

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“…Hu et al (2020) and Chen et al (2021b) propose systems which perform single-sentence natural language inference through proof search in the natural logic space. Explicitly using the monotonicity calculus (Icard et al, 2017) and natural logic to generate contrastive examples for semisynthetic mid-training is a promising future direction that could help to address the monotonicity issues encountered by our step deduction model, as discussed in Section 5.4. Our work also relates to earlier efforts on natural logic (MacCartney and Manning, 2009;Angeli et al, 2016) but is able to cover far more phenomena by relaxing the strict constraints of this framework.…”

Section: Related Workmentioning

confidence: 99%

Natural Language Deduction through Search over Statement Compositions

Bostrom¹,

Sprague²,

Chaudhuri³

et al. 2022

Preprint

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In settings from fact-checking to question answering, we frequently want to know whether a collection of evidence entails a hypothesis. Existing methods primarily focus on end-toend discriminative versions of this task, but less work has treated the generative version in which a model searches over the space of entailed statements to derive the hypothesis. We propose a system for natural language deduction that decomposes the task into separate steps coordinated by best-first search, producing a tree of intermediate conclusions that faithfully reflects the system's reasoning process. Our experiments demonstrate that the proposed system can better distinguish verifiable hypotheses from unverifiable ones and produce natural language explanations that are more internally consistent than those produced by an end-to-end T5 model.

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Section: Related Workmentioning

confidence: 99%

Natural Language Deduction through Search over Statement Compositions

Bostrom¹,

Sprague²,

Chaudhuri³

et al. 2022

Preprint

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“…It is this final monotonicity la- bel that determines the entailment patterns with respect to insertion relations. Although there are formalisms that model this logical behaviour (Icard et al, 2017), they aim to model the behaviour of each linguistic linguistic operator and the way they compose given the parse tree of a sentence.…”

Section: Monotonicitymentioning

confidence: 99%

“…Only the following are considered sentences in the language L: This can in many ways be seen as a simplification of previous formalisms (Icard et al, 2017;Hu and Moss, 2018) based on either extending the syllogistic logic L(all) (Moss, 2008a) or extending typed lambda calculus with monotonicity behaviour. The key difference of this approach is the abstraction away from specific linguistic operators and their monotonicity profiles.…”

Section: Exactly Two Variables X and Ymentioning

confidence: 99%

“…The study of monotonicity in natural language has a strongly developed linguistic and mathematical theoretical groundwork, dating back to the monotonicity calculus of (Sanchez, 1991) and in semantic studies such as (Van Benthem et al, 1986). Its formal treatments have led to the expansion of typed lambda calculus with an order relation so as to model this order-theoretic behaviour, resulting in a corresponding deduction system and completeness theorem in (Icard et al, 2017). There are varying presentations and some variation in terminology, but for the most part monotonicity refers to the order-theoretic property of the context as a function, while the term polarity usually refers to the tag assigned to the node in a CCG parse tree or a word in a sentence.…”

Section: Related Workmentioning

confidence: 99%

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Supporting Context Monotonicity Abstractions in Neural NLI Models

Rozanova¹,

Ferreira²,

Thayaparan³

et al. 2021

Preprint

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Natural language contexts display logical regularities with respect to substitutions of related concepts: these are captured in a functional order-theoretic property called monotonicity. For a certain class of NLI problems where the resulting entailment label depends only on the context monotonicity and the relation between the substituted concepts, we build on previous techniques that aim to improve the performance of NLI models for these problems, as consistent performance across both upward and downward monotone contexts still seems difficult to attain even for state of the art models. To this end, we reframe the problem of context monotonicity classification to make it compatible with transformer-based pre-trained NLI models and add this task to the training pipeline. Furthermore, we introduce a sound and complete simplified monotonicity logic formalism which describes our treatment of contexts as abstract units. Using the notions in our formalism, we adapt targeted challenge sets to investigate whether an intermediate context monotonicity classification task can aid NLI models' performance on examples exhibiting monotonicity reasoning.

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“…Predication as a source of ordering statements A sentence like Whiskers is a cat gives us inequalities to put into a knowledge base: every cat ≤ Whiskers, and also Whiskers ≤ some cat. Note that we want to permit ≤ statements between different ordered types, but those types must be in an appropriate relation called ; see [4,5].…”

Section: Substitution As Inference: An Examplementioning

confidence: 99%

Automated Reasoning from Polarized Parse Trees

Hu¹,

Icard²,

Moss³

2018

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This paper contributes to symbolic inference from text, including naturally occurring text. The idea is to take sentences in a framework like CCG, and then run a polarizing algorithm like the one in Hu and Moss 2018 to determine inferential polarity markings of all the constituents. From this, it is just a small step to obtain an inference engine which is both simple to describe and implement and at the same time is surprisingly powerful. We have implemented the basic inference step. This paper is work in progress, also going into detail on our projected next steps. The overall goal is to have a working symbolic inference system which covers "in-practice" inference and also is correct and efficient.

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A Monotonicity Calculus and Its Completeness

Cited by 9 publications

References 19 publications

Natural Language Deduction through Search over Statement Compositions

Natural Language Deduction through Search over Statement Compositions

Supporting Context Monotonicity Abstractions in Neural NLI Models

Automated Reasoning from Polarized Parse Trees

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