Fuzzy inequational logic

We present a logic for reasoning about graded inequalities which generalizes the ordinary inequational logic used in universal algebra. The logic deals with atomic predicate formulas of the form of inequalities between terms and formalizes their semantic entailment and provability in graded setting which allows to draw partially true conclusions from partially true assumptions. We follow the Pavelka approach and define general degrees of semantic entailment and provability using complete residuated lattices as structures of truth degrees. We prove the logic is Pavelka-style complete. Furthermore, we present a logic for reasoning about graded if-then rules which is obtained as particular case of the general result

MonaLog: a Lightweight System for Natural Language Inference Based on Monotonicity

We present a new logic-based inference engine for natural language inference called MonaLog, which is based on the monotonicity calculus and natural logic. In contrast to existing logic-based approaches, our system is lightweight, and operates using a small set of well-known monotonicity facts about quantifiers and lexical items. Despite its simplicity, we find it competitive with other logic-based NLI models on the SICK benchmark. We also use MonaLog incombination with BERT in a variety of settings, including data augmentation. We show that MonaLog is capable of generating large amounts of high-quality training data for BERT, improving its accuracy on SICK

Noncomparabilities & Non Standard Logics

Many normative theories set forth in the welfare economics, distributive justice and cognate literatures posit noncomparabilities or incommensurabilities between magnitudes of various kinds. In some cases these gaps are predicated on metaphysical claims, in others upon epistemic claims, and in still others upon political-moral claims. I show that in all such cases they are best given formal expression in nonstandard logics that reject bivalence, excluded middle, or both. I do so by reference to an illustrative case study: a contradiction known to beset John Rawls\u27s selection and characterization of primary goods as the proper distribuendum in any distributively just society. The contradiction is avoided only by reformulating Rawls\u27s claims in a nonstandard form, which form happens also to cohere quite attractively with Rawls\u27s intuitive argumentation on behalf of his claims

Noncomparabilities & Non Standard Logics

Many normative theories set forth in the welfare economics, distributive justice and cognate literatures posit noncomparabilities or incommensurabilities between magnitudes of various kinds. In some cases these gaps are predicated on metaphysical claims, in others upon epistemic claims, and in still others upon political-moral claims. I show that in all such cases they are best given formal expression in nonstandard logics that reject bivalence, excluded middle, or both. I do so by reference to an illustrative case study: a contradiction known to beset John Rawls\u27s selection and characterization of primary goods as the proper distribuendum in any distributively just society. The contradiction is avoided only by reformulating Rawls\u27s claims in a nonstandard form, which form happens also to cohere quite attractively with Rawls\u27s intuitive argumentation on behalf of his claims

Inconsistencies Detection in Bipolar Entailment Graphs

International audienceEnglish. In the latest years, a number of real world applications have underlined the need to move from Textual Entailment (TE) pairs to TE graphs where pairs are no more independent. Moving from single pairs to a graph has the advantage of providing an overall view of the issue discussed in the text, but this may lead to possible inconsistencies due to the combination of the TE pairs into a unique graph. In this paper, we adopt argumentation theory to support human annotators in detecting the possible sources of inconsistencies. Italiano. Negli ultimi anni, in svari-ate applicazioni sta sorgendo la necessit a di passare da coppie di Textual Entail-ment (TE) a grafi di TE, in cui le cop-pie sono interconnesse. Il vantaggio dei grafi di TE e di fornire una visione glob-ale del soggetto di cui si sta discutendo nel testo. Allo stesso tempo, questopù o gener-are inconsistenze dovute all'integrazione dipì u coppie di TE in un unico grafo. In questo articolo, ci basiamo sulla teo-ria dell'argomentazione per supportare gli annotatori nell'individuare le possibili fonti di inconsistenze

A Transformation-based Implementation for CLP with Qualification and Proximity

Uncertainty in logic programming has been widely investigated in the last decades, leading to multiple extensions of the classical LP paradigm. However, few of these are designed as extensions of the well-established and powerful CLP scheme for Constraint Logic Programming. In a previous work we have proposed the SQCLP (proximity-based qualified constraint logic programming) scheme as a quite expressive extension of CLP with support for qualification values and proximity relations as generalizations of uncertainty values and similarity relations, respectively. In this paper we provide a transformation technique for transforming SQCLP programs and goals into semantically equivalent CLP programs and goals, and a practical Prolog-based implementation of some particularly useful instances of the SQCLP scheme. We also illustrate, by showing some simple-and working-examples, how the prototype can be effectively used as a tool for solving problems where qualification values and proximity relations play a key role. Intended use of SQCLP includes flexible information retrieval applications.Comment: 49 pages, 5 figures, 1 table, preliminary version of an article of the same title, published as Technical Report SIC-4-10, Universidad Complutense, Departamento de Sistemas Inform\'aticos y Computaci\'on, Madrid, Spai

Intertheoretic Reduction, Confirmation, and Montague’s Syntax-Semantics Relation

Intertheoretic relations are an important topic in the philosophy of science. However, since their classical discussion by Ernest Nagel, such relations have mostly been restricted to relations between pairs of theories in the natural sciences. This paper presents a case study of a new type of intertheoretic relation that is inspired by Montague's analysis of the linguistic syntax-semantics relation. The paper develops a simple model of this relation. To motivate the adoption of our new model, we show that this model extends the scope of application of the Nagelian (or related) models and that it shares the epistemological advantages of the Nagelian model. The latter is achieved in a Bayesian framework