Entailment Relation Research Articles

Subset Realization and the Entailment Problem in advance

According to the principle of conditional power aggregation (CPA), conditional powers conjoin when the properties that bestow them conjoin. Sophie Gibb has argued that CPA is false given Shoemaker’s account of conditional powers and that this leads to a problem for his account of subset realization. In short: If CPA is rejected, subset realization fails to be an entailment relation, in which case it cannot provide a basis for non-reductive physicalism. I defend the subset account against this argument by denying that CPA fails. I argue that (i) Shoemaker’s account of conditional powers does not warrant a rejection of CPA, (ii) his account is incomplete and should be supplemented with a further sufficient condition for when a property bestows a conditional power, and (iii) this further sufficient condition supports CPA.

Quantifying Satisfaction of Security Requirements of Cloud Software Systems

The satisfaction of a software requirement is commonly stated as a Boolean value, that is, a security requirement is either satisfied (true) or not (false). However, a discrete Boolean value to measure the satisfaction level of a security requirement by deployed mechanisms is not very useful. Rather, it would be more effective if we could quantify the level of satisfaction of security requirements on a continuous scale. We propose an approach to achieve this for cloud software systems based on relationships between defense strength, exploitability of vulnerabilities, and attack severity. We extend the concept of entailment relationship from the field of requirements engineering with the satisfiability aspects of security requirements. The proposed approach enables us to systematically structure security concepts into three sets of related descriptions to quantify the satisfaction level of security requirements with the deployed security solutions. To demonstrate the feasibility of the proposed approach, we evaluate the approach in a case study. As a result, security administrators are able to deploy more effective and appropriate security solutions based on their assessment.

A formal approach to Menger's theorem

Menger's graph theorem equates the minimum size of a separating set for non-adjacent vertices a and b with the maximum number of disjoint paths between a and b. By capturing separating sets as models of an entailment relation, we take a formal approach to Menger's result. Upon showing that inconsistency is characterised by the existence of suficiently many disjoint paths, we recover Menger's theorem by way of completeness.

PROBABILISTIC ENTAILMENT ON FIRST ORDER LANGUAGES AND REASONING WITH INCONSISTENCIES

AbstractWe investigate an approach for drawing logical inference from inconsistent premisses. The main idea in this approach is that the inconsistencies in the premisses should be interpreted as uncertainty of the information. We propose a mechanism, based on Kinght’s [14] study of inconsistency, for revising an inconsistent set of premisses to a minimally uncertain, probabilistically consistent one. We will then generalise the probabilistic entailment relation introduced in [15] for propositional languages to the first order case to draw logical inference from a probabilistic set of premisses. We will show how this combination can allow us to limit the effect of uncertainty introduced by inconsistent premisses to only the reasoning on the part of the premise set that is relevant to the inconsistency.

Entailment Relation Aware Paraphrase Generation

We introduce a new task of entailment relation aware paraphrase generation which aims at generating a paraphrase conforming to a given entailment relation (e.g. equivalent, forward entailing, or reverse entailing) with respect to a given input. We propose a reinforcement learning-based weakly-supervised paraphrasing system, ERAP, that can be trained using existing paraphrase and natural language inference (NLI) corpora without an explicit task-specific corpus. A combination of automated and human evaluations show that ERAP generates paraphrases conforming to the specified entailment relation and are of good quality as compared to the baselines and uncontrolled paraphrasing systems. Using ERAP for augmenting training data for downstream textual entailment task improves performance over an uncontrolled paraphrasing system, and introduces fewer training artifacts, indicating the benefit of explicit control during paraphrasing.

Counterfactuals, hyperintensionality and Hurford disjunctions

This paper investigates propositional hyperintensionality in counterfactuals. It starts with a scenario describing two children playing on a seesaw and studies the truth-value predictions for counterfactuals by four different semantic theories. The theories in question are Kit Fine’s truthmaker semantics, Luis Alonso-Ovalle’s alternative semantics, inquisitive semantics and Paolo Santorio’s syntactic truthmaker semantics. These predictions suggest that the theories that distinguish more of a given set of intensionally equivalent sentences (Fine and Alonso-Ovalle’s) fare better than those that do not (inquisitive semantics and Santorio’s). Then we investigate how inquisitive semantics and Santorio can respond to these results. They can respond to them by helping themselves to considerations from Hurford disjunctions, disjunctions whose disjuncts stand in an entailment relation to one another. I argue that considerations from Hurford disjunctions are ad hoc modifications to less fine-grained theories to predict the expected results and they are not independently motivated. I conclude that the scenarios suggest a need for more fine-grained theories of sentential meaning in general.

Overview and Discussion of the Competition on Legal Information Extraction/Entailment (COLIEE) 2021

We summarize the 8th Competition on Legal Information Extraction and Entailment. In this edition, the competition included five tasks on case law and statute law. The case law component includes an information retrieval Task (Task 1), and the confirmation of an entailment relation between an existing case and an unseen case (Task 2). The statute law component includes an information retrieval Task (Task 3), an entailment/question answering task based on retrieved civil code statutes (Task 4) and an entailment/question answering task without retrieved civil code statutes (Task 5). Participation was open to any group based on any approach. Eight different teams participated in the case law competition tasks, most of them in more than one task. We received results from six teams for Task 1 (16 runs) and 6 teams for Task 2 (17 runs). On the statute law task, there were eight different teams participating, most in more than one task. Six teams submitted a total of 18 runs for Task 3, 6 teams submitted a total of 18 runs for Task 4, and 4 teams submitted a total of 12 runs for Task 5. Here we summarize the approaches, our official evaluation, and analysis on our data and submission results.

Intensional Semantics for Syllogistics: what Leibniz and Vasiliev Have in Common

This article deals with an alternative interpretation of syllogistics, different from the classical (extensional) one: an intensional one, in which subject and predicate are not associated with a set of individuals (the extension of the concept) but a set of attributes (the content of the concept). The authors of the paper draw attention to the fact that this approach was first proposed by Leibniz in works on logical calculus, which for a long time remained in the shadow of his other philosophical works. Currently, the intensional approach is gaining more and more popularity due to the development of non-classical logics, and the article will present several existing intensional formal syllogistic semantics. The paper will also consider another historical approach to syllogistics, associated with the name of the Russian logician Nikolai Vasiliev, who is not only one of the founders of non-classical (non-Aristotelian logic) but also of a different intensional interpretation of such logic. The authors, along with the already known formalizations of Vasiliev’s ideas, present two new systems. One of them is a reconstruction of one type of imaginary logic with statements of three qualities: affirmative and two types of negative statements (with absolute and ordinary negation). The second system is the one that is adequate to semantics, in which instead of the four classical ones, only three types of statements are presented (two particular statements are replaced by one - accidental), and their significance is determined through the relation of the classical logical entailment. Both of them are interpreted intensionally. The intensional approach in logic and, in particular, in syllogistics allows us to expand the class of accepted principles (which occurs due to the expansion of the class of correct moods of syllogisms).

Evidence-Aware Multilingual Fake News Detection

Due to the rapid growth of the Internet and the subsequent rise of social media users, sharing information has become more flexible than ever before. This unrestricted freedom has also led to an increase in fake news. During the Covid-19 outbreak, fake news spread globally, negatively affecting authorities’ decisions and the health of individuals. As a result, governments, media agencies, and academics have established fact-checking units and developed automatic detection systems. Research approaches focused largely on writing styles, propagation patterns, and building knowledge bases that serve as a reference for fact checking. However, little work has been done to assess the credibility of the source of the claim to be checked. This paper proposes a general framework for detecting fake news that uses external evidence to verify the veracity of online news in a multilingual setting. Search results from Google are used as evidence, and the claim is cross-checked with the top five search results. Additionally, we associate a vector of credibility scores with each evidence source based on the domain name and website reputation metrics. All of these components are combined to derive better predictions of the veracity of claims. Further, we analyze the claim-evidence entailment relationship and select supporting and refuting evidence to cross-check with the claim. The selection free approach yields better detection performance. In this work, we consider as a case study Covid-19 related news. Our framework achieves an F1-score of 0.85 and 0.97 in distinguishing fake from true news on XFact and Constraint datasets respectively. With the achieved results, the proposed framework present a promising automatic fact checker for both early and late detection.

Dynamic Probabilistic Entailment. Improving on Adams' Dynamic Entailment Relation

The inferences of contraposition (A ⇒ C ∴ ¬C ⇒ ¬A), the hypothetical syllogism (A ⇒ B, B ⇒ C ∴ A ⇒ C), and others are widely seen as unacceptable for counterfactual conditionals. Adams convincingly argued, however, that these inferences are unacceptable for indicative conditionals as well. He argued that an indicative conditional of form A ⇒ C has assertability conditions instead of truth conditions, and that their assertability ‘goes with’ the conditional probability p(C|A). To account for inferences, Adams developed the notion of probabilistic entailment as an extension of classical entailment. This combined approach (correctly) predicts that contraposition and the hypothetical syllogism are invalid inferences. Perhaps less well-known, however, is that the approach also predicts that the unconditional counterparts of these inferences, e.g., modus tollens (A ⇒ C, ¬C ∴ ¬A), and iterated modus ponens (A ⇒ B, B ⇒ C, A ∴ C) are predicted to be valid. We will argue both by example and by calling to the results from a behavioral experiment (N = 159) that these latter predictions are incorrect if the unconditional premises in these inferences are seen as new information. Then we will discuss Adams’ (1998) dynamic probabilistic entailment relation, and argue that it is problematic. Finally, it will be shown how his dynamic entailment relation can be improved such that the incongruence predicted by Adams’ original system concerning conditionals and their unconditional counterparts are overcome. Finally, it will be argued that the idea behind this new notion of entailment is of more general relevance.

THE JACOBSON RADICAL OF A PROPOSITIONAL THEORY

AbstractAlongside the analogy between maximal ideals and complete theories, the Jacobson radical carries over from ideals of commutative rings to theories of propositional calculi. This prompts a variant of Lindenbaum’s Lemma that relates classical validity and intuitionistic provability, and the syntactical counterpart of which is Glivenko’s Theorem. The Jacobson radical in fact turns out to coincide with the classical deductive closure. As a by-product we obtain a possible interpretation in logic of the axioms-as-rules conservation criterion for a multi-conclusion Scott-style entailment relation over a single-conclusion one.

Formalizing Reasons, Oughts, and Requirements

Reasons-based accounts of our normative conclusions face difficulties in distinguishing between what ought to be done and what is required. This article addresses this problem from a formal perspective. I introduce a rudimentary formalization of a reasons-based account and demonstrate that that the model faces difficulties in accounting for the distinction between oughts and requirements. I briefly critique attempts to distinguish between oughts and requirements by appealing to a difference in strength or weight of reasons. I then present a formalized reasons-based account of permissions, oughts and requirements. The model exploits Joshua Gert (2004; 2007) and Patricia Greenspan’s (2005; 2007; 2010) suggestion that some reasons perform a purely justificatory function. I show that the model preserves the standard entailment relationships between requirements, oughts and permissions.

ArGoT: A Glossary of Terms extracted from the arXiv

We introduce ArGoT, a data set of mathematical terms extracted from the articles hosted on the arXiv website. A term is any mathematical concept defined in an article. Using labels in the article's source code and examples from other popular math websites, we mine all the terms in the arXiv data and compile a comprehensive vocabulary of mathematical terms. Each term can be then organized in a dependency graph by using the term's definitions and the arXiv's metadata. Using both hyperbolic and standard word embeddings, we demonstrate how this structure is reflected in the text's vector representation and how they capture relations of entailment in mathematical concepts. This data set is part of an ongoing effort to align natural mathematical text with existing Interactive Theorem Prover Libraries (ITPs) of formally verified statements.

Modal Logic S5 Satisfiability in Answer Set Programming

AbstractModal logic S5 has attracted significant attention and has led to several practical applications, owing to its simplified approach to dealing with nesting modal operators. Efficient implementations for evaluating satisfiability of S5 formulas commonly rely on Skolemisation to convert them into propositional logic formulas, essentially by introducing copies of propositional atoms for each set of interpretations (possible worlds). This approach is simple, but often results into large formulas that are too difficult to process, and therefore more parsimonious constructions are required. In this work, we propose to use Answer Set Programming for implementing such constructions, and in particular for identifying the propositional atoms that are relevant in every world by means of a reachability relation. The proposed encodings are designed to take advantage of other properties such as entailment relations of subformulas rooted by modal operators. An empirical assessment of the proposed encodings shows that the reachability relation is very effective and leads to comparable performance to a state-of-the-art S5 solver based on SAT, while entailment relations are possibly too expensive to reason about and may result in overhead.

A generative adversarial network for single and multi-hop distributional knowledge base completion

Knowledge bases (KBs) inherently lack reasoning ability, limiting their effectiveness for tasks such as question–answering and query expansion. Machine-learning is hence commonly employed for representation learning in order to learn semantic features useful for generalization. Most existing methods utilize discriminative models that require both positive and negative samples to learn a decision boundary. KBs, by contrast, contain only positive samples, necessitating that negative samples are generated by replacing the head/tail of predicates with randomly-chosen entities. They are thus frequently easily discriminable from positive samples, which can prevent learning of sufficiently robust classifiers.Generative models, however, do not require negative samples to learn the distribution of positive samples; stimulated by recent developments in Generative Adversarial Networks (GANs), we propose a novel framework, Knowledge Completion GANs (KCGANs), for competitively training generative link prediction models against discriminative belief prediction models. KCGAN thus invokes a game between generator-network G and discriminator-network D in which G aims to understand underlying KB structure by learning to perform link prediction while D tries to gain knowledge about the KB by learning predicate/triplet classification. Two key challenges are addressed: 1) Classical GAN architectures’ inability to easily generate samples over discrete entities; 2) the inefficiency of softmax for learning distributions over large sets of entities. As a step toward full first-order logical reasoning we further extend KCGAN to learn multi-hop logical entailment relations between entities by enabling G to compose a multi-hop relational path between entities and D to discriminate between real and fake paths.KCGAN is tested on benchmarks WordNet and FreeBase datasets and evaluated on link prediction and belief prediction tasks using MRR and HIT@ 10, achieving best-in-class performance.

Contextual Conditional Reasoning

We extend the expressivity of classical conditional reasoning by introducing context as a new parameter. The enriched conditional logic generalises the defeasible setting in the style of Kraus, Lehmann and Magidor, and allows for a more refined representation of an agent’s epistemic state, distinguishing, for example, between expectations and counterfactuals. In this paper we introduce the language for the enriched logic, and define an appropriate semantic framework for it. We analyse which properties generally associated with conditional reasoning are still satisfied by the new semantic framework, provide an appropriate representation result, and define an entailment relation based on Lehmann and Magidor’s notion of Rational Closure.

Natural Language Inference in Context - Investigating Contextual Reasoning over Long Texts

Natural language inference (NLI) is a fundamental NLP task, investigating the entailment relationship between two texts. Popular NLI datasets present the task at sentence-level. While adequate for testing semantic representations, they fall short for testing contextual reasoning over long texts, which is a natural part of the human inference process. We introduce ConTRoL, a new dataset for ConTextual Reasoning over Long texts. Consisting of 8,325 expert-designed "context-hypothesis" pairs with gold labels, ConTRoL is a passage-level NLI dataset with a focus on complex contextual reasoning types such as logical reasoning. It is derived from competitive selection and recruitment test (verbal reasoning test) for police recruitment, with expert level quality. Compared with previous NLI benchmarks, the materials in ConTRoL are much more challenging, involving a range of reasoning types. Empirical results show that state-of-the-art language models perform by far worse than educated humans. Our dataset can also serve as a testing-set for downstream tasks like checking the factual correctness of summaries.

Deep Artificial Neural Networks Reveal a Distributed Cortical Network Encoding Propositional Sentence-Level Meaning.

Understanding how and where in the brain sentence-level meaning is constructed from words presents a major scientific challenge. Recent advances have begun to explain brain activation elicited by sentences using vector models of word meaning derived from patterns of word co-occurrence in text corpora. These studies have helped map out semantic representation across a distributed brain network spanning temporal, parietal, and frontal cortex. However, it remains unclear whether activation patterns within regions reflect unified representations of sentence-level meaning, as opposed to superpositions of context-independent component words. This is because models have typically represented sentences as "bags-of-words" that neglect sentence-level structure. To address this issue, we interrogated fMRI activation elicited as 240 sentences were read by 14 participants (9 female, 5 male), using sentences encoded by a recurrent deep artificial neural-network trained on a sentence inference task (InferSent). Recurrent connections and nonlinear filters enable InferSent to transform sequences of word vectors into unified "propositional" sentence representations suitable for evaluating intersentence entailment relations. Using voxelwise encoding modeling, we demonstrate that InferSent predicts elements of fMRI activation that cannot be predicted by bag-of-words models and sentence models using grammatical rules to assemble word vectors. This effect occurs throughout a distributed network, which suggests that propositional sentence-level meaning is represented within and across multiple cortical regions rather than at any single site. In follow-up analyses, we place results in the context of other deep network approaches (ELMo and BERT) and estimate the degree of unpredicted neural signal using an "experiential" semantic model and cross-participant encoding.SIGNIFICANCE STATEMENT A modern-day scientific challenge is to understand how the human brain transforms word sequences into representations of sentence meaning. A recent approach, emerging from advances in functional neuroimaging, big data, and machine learning, is to computationally model meaning, and use models to predict brain activity. Such models have helped map a cortical semantic information-processing network. However, how unified sentence-level information, as opposed to word-level units, is represented throughout this network remains unclear. This is because models have typically represented sentences as unordered "bags-of-words." Using a deep artificial neural network that recurrently and nonlinearly combines word representations into unified propositional sentence representations, we provide evidence that sentence-level information is encoded throughout a cortical network, rather than in a single region.

The free energy principle: it’s not about what it takes, it’s about what took you there

Philosophical writings on the free energy principle in the life sciences often give the impression that minimising free energy is sufficient for life. But minimising free energy is not a sufficient condition for life. In fact, one can perfectly well conceive of a system that actively minimises its free energy, and for this very reason moves inexorably towards death. So, where does the assumption of this entailment relation come from? There is indeed an entailment relation, but it goes the other way around: life entails minimising free energy. Put another way, if you exist, now, under the right conditions, it is because you’ve done something like minimising your free energy. However, the question of whether you will exist tomorrow cannot be settled purely by resorting to the fact that you will minimise your free energy to get there. The simple point I make in this paper is that the free energy principle is not concerned with the sufficient conditions of existence, but rather with what must have been the case, given that you exist. It’s not about figuring out what it takes to be alive; it’s about figuring out what took you there.

PE-MSC: partial entailment-based minimum set cover for text summarization

The notion of Textual Entailment (TE) is an established indicator of text connectedness. It captures semantic relationships between texts. Recently, it has been used successfully for determining sentence salience in many text summarization methods. However, it has been reported in previous works that the standard textual entailment is not ideal for measuring sentence salience. This is because textual entailment relationships between sentences are quite rare in real-world texts. Therefore, we suggest using partial TE to accomplish the task of recognizing standard TE. We present the single document summarization problem as an optimization problem which is solved using a weighted Minimum Set Cover (wMSC) algorithm. In this method, sentences are broken into fragments and Partial TE is used to form sets of fragments. Finally, wMSC is applied to the sets to obtain the minimum set cover, which corresponds to the summary of the document. The results achieved on the DUC 2002 dataset using ROUGE and other quality metrics show that the proposed method outperforms the state of the art.