Description Logics Go Second-Order -- Extending EL with Universally Quantified Concepts

• URL: http://arxiv.org/abs/2308.08252v2
• Date: Tue, 29 Aug 2023 13:32:40 GMT
• Title: Description Logics Go Second-Order -- Extending EL with Universally Quantified Concepts
• Authors: Joshua Hirschbrunn and Yevgeny Kazakov
• Abstract summary: We focus on the extension of description logic $mathcalEL$. We show that for a useful fragment of the extension, the conclusions entailed by the different semantics coincide. For a slightly smaller, but still useful, fragment, we were also able to show decidability of the extension.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The study of Description Logics have been historically mostly focused on features that can be translated to decidable fragments of first-order logic. In this paper, we leave this restriction behind and look for useful and decidable extensions outside first-order logic. We introduce universally quantified concepts, which take the form of variables that can be replaced with arbitrary concepts, and define two semantics of this extension. A schema semantics allows replacements of concept variables only by concepts from a particular language, giving us axiom schemata similar to modal logics. A second-order semantics allows replacement of concept variables with arbitrary subsets of the domain, which is similar to quantified predicates in second-order logic. To study the proposed semantics, we focus on the extension of the description logic $\mathcal{EL}$. We show that for a useful fragment of the extension, the conclusions entailed by the different semantics coincide, allowing us to use classical $\mathcal{EL}$ reasoning algorithms even for the second-order semantics. For a slightly smaller, but still useful, fragment, we were also able to show polynomial decidability of the extension. This fragment, in particular, can express a generalized form of role chain axioms, positive self restrictions, and some forms of (local) role-value-maps from KL-ONE, without requiring any additional constructors.

Related papers

• LogicBench: Towards Systematic Evaluation of Logical Reasoning Ability of Large Language Models [52.03659714625452]
  Recently developed large language models (LLMs) have been shown to perform remarkably well on a wide range of language understanding tasks. But, can they really "reason" over the natural language? This question has been receiving significant research attention and many reasoning skills such as commonsense, numerical, and qualitative have been studied.
  arXiv  Detail & Related papers  (2024-04-23T21:08:49Z)
• The Transformation Logics [58.35574640378678]
  We introduce a new family of temporal logics designed to balance the trade-off between expressivity and complexity. Key feature is the possibility of defining operators of a new kind that we call transformation operators. We show them to yield logics capable of creating hierarchies of increasing expressivity and complexity.
  arXiv  Detail & Related papers  (2023-04-19T13:24:04Z)
• Zero-Shot Classification by Logical Reasoning on Natural Language Explanations [56.42922904777717]
  We propose the framework CLORE (Classification by LOgical Reasoning on Explanations) CLORE parses explanations into logical structures and then explicitly reasons along thess structures on the input to produce a classification score. We also demonstrate that our framework can be extended to zero-shot classification on visual modality.
  arXiv  Detail & Related papers  (2022-11-07T01:05:11Z)
• Discourse-Aware Graph Networks for Textual Logical Reasoning [142.0097357999134]
  Passage-level logical relations represent entailment or contradiction between propositional units (e.g., a concluding sentence) We propose logic structural-constraint modeling to solve the logical reasoning QA and introduce discourse-aware graph networks (DAGNs) The networks first construct logic graphs leveraging in-line discourse connectives and generic logic theories, then learn logic representations by end-to-end evolving the logic relations with an edge-reasoning mechanism and updating the graph features.
  arXiv  Detail & Related papers  (2022-07-04T14:38:49Z)
• How to Agree to Disagree: Managing Ontological Perspectives using Standpoint Logic [2.9005223064604073]
  Standpoint Logic is a simple, yet versatile multi-modal logic add-on'' for existing KR languages. We provide a polytime translation into the standpoint-free version of First-Order Standpoint Logic. We then establish a similar translation for the very expressive description logic SROIQb_s underlying the OWL 2 DL language.
  arXiv  Detail & Related papers  (2022-06-14T12:29:08Z)
• Reasoning in the Description Logic ALC under Category Semantics [0.0]
  We present a reformulation of the usual set-theoretical semantics of the description logic $mathcalALC$ with general TBoxes by using categorical language. In this setting, $mathcalALC$ concepts are represented as objects, concept subsumptions as arrows, and memberships as logical quantifiers over objects and arrows of categories.
  arXiv  Detail & Related papers  (2022-05-10T14:03:44Z)
• Logic-Driven Context Extension and Data Augmentation for Logical Reasoning of Text [65.24325614642223]
  We propose to understand logical symbols and expressions in the text to arrive at the answer. Based on such logical information, we put forward a context extension framework and a data augmentation algorithm. Our method achieves the state-of-the-art performance, and both logic-driven context extension framework and data augmentation algorithm can help improve the accuracy.
  arXiv  Detail & Related papers  (2021-05-08T10:09:36Z)
• Lexicographic Logic: a Many-valued Logic for Preference Representation [1.5484595752241122]
  We propose lexicographic logic, an extension of classical propositional logic that can express a variety of preferences. We argue that the new logic is an effective formalism for ranking query results according to the satisfaction level of user preferences.
  arXiv  Detail & Related papers  (2020-12-20T14:42:04Z)
• Logical Neural Networks [51.46602187496816]
  We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning) Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a highly intepretable disentangled representation. Inference is omni rather than focused on predefined target variables, and corresponds to logical reasoning.
  arXiv  Detail & Related papers  (2020-06-23T16:55:45Z)
• Reasoning about Typicality and Probabilities in Preferential Description Logics [0.15749416770494704]
  We describe preferential Description Logics of typicality, a nonmonotonic extension of standard Description Logics by means of a typicality operator T. This extension is based on a minimal model semantics corresponding to a notion of rational closure. We consider other strengthening of the rational closure semantics and construction to avoid the so-called blocking of property inheritance problem.
  arXiv  Detail & Related papers  (2020-04-20T14:50:31Z)
• Intuitionistic Linear Temporal Logics [0.7087237546722617]
  We consider intuitionistic variants of linear temporal logic with next', until' and release' We prove that $iltl$ has the effective finite model property and hence is decidable, while $itlb$ does not have the finite model property. We also introduce notions of bounded bisimulations for these logics and use them to show that the until' and release' operators are not definable in terms of each other, even over the class of persistent posets.
  arXiv  Detail & Related papers  (2019-12-30T11:49:31Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.