Avoiding Pragmatic Oddity: A Bottom-up Defeasible Deontic Logic
- URL: http://arxiv.org/abs/2209.04553v1
- Date: Fri, 9 Sep 2022 23:14:09 GMT
- Title: Avoiding Pragmatic Oddity: A Bottom-up Defeasible Deontic Logic
- Authors: Guido Governatori, Silvano Colombo Tosatto and Antonino Rotolo
- Abstract summary: This paper presents an extension of Defeasible Deontic Logic to deal with the Pragmatic Oddity problem.
The logic applies three general principles: (1) the Pragmatic Oddity problem must be solved within a general logical treatment of CTD reasoning; (2) non-monotonic methods must be adopted to handle CTD reasoning; and (3) logical models of CTD reasoning must be computationally feasible and, if possible, efficient.
- Score: 1.160208922584163
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: This paper presents an extension of Defeasible Deontic Logic to deal with the
Pragmatic Oddity problem. The logic applies three general principles: (1) the
Pragmatic Oddity problem must be solved within a general logical treatment of
CTD reasoning; (2) non-monotonic methods must be adopted to handle CTD
reasoning; (3) logical models of CTD reasoning must be computationally feasible
and, if possible, efficient. The proposed extension of Defeasible Deontic Logic
elaborates a preliminary version of the model proposed by Governatori and
Rotolo (2019). The previous solution was based on particular characteristics of
the (constructive, top-down) proof theory of the logic. However, that method
introduces some degree of non-determinism. To avoid the problem, we provide a
bottom-up characterisation of the logic. The new characterisation offers
insights for the efficient implementation of the logic and allows us to
establish the computational complexity of the problem.
Related papers
- Towards Propositional KLM-Style Defeasible Standpoint Logics [3.8097021295196414]
We introduce the logical system of Defeasible Restricted Standpoint Logic (DRSL) and define its syntax and semantics.
Specifically, we integrate ranked interpretations and standpoint structures, which provide the semantics for propositional KLM and propositional standpoint logic respectively.
We extend the non-monotonic entailment relation of rational closure from the propositional KLM case to the DRSL case.
arXiv Detail & Related papers (2024-10-05T18:07:03Z) - Towards Generalizable and Faithful Logic Reasoning over Natural Language via Resolution Refutation [24.584926992534346]
We propose a novel framework, named Generalizable and Faithful Reasoner (GFaiR), which introduces the paradigm of resolution refutation.
Resolution refutation has the capability to solve all first-order logic reasoning problems by extending reasoning rules and employing the principle of proof by contradiction.
Our system outperforms previous works by achieving state-of-the-art performances in complex scenarios while maintaining performances in simple scenarios.
arXiv Detail & Related papers (2024-04-02T06:28:44Z) - Language Models can be Logical Solvers [99.40649402395725]
We introduce LoGiPT, a novel language model that directly emulates the reasoning processes of logical solvers.
LoGiPT is fine-tuned on a newly constructed instruction-tuning dataset derived from revealing and refining the invisible reasoning process of deductive solvers.
arXiv Detail & Related papers (2023-11-10T16:23:50Z) - An elementary belief function logic [6.091096843566857]
duality between possibility and necessity measures, belief and plausibility functions and imprecise probabilities share a common feature with modal logic.
This paper shows that a simpler belief function logic can be devised by adding Lukasiewicz logic on top of MEL.
arXiv Detail & Related papers (2023-03-23T10:39:18Z) - Non-Deterministic Approximation Fixpoint Theory and Its Application in
Disjunctive Logic Programming [11.215352918313577]
Approximation fixpoint theory is a framework for studying the semantics of nonmonotonic logics.
We extend AFT to dealing with non-deterministic constructs that allow to handle indefinite information.
The applicability and usefulness of this generalization is illustrated in the context of disjunctive logic programming.
arXiv Detail & Related papers (2022-11-30T18:58:32Z) - MetaLogic: Logical Reasoning Explanations with Fine-Grained Structure [129.8481568648651]
We propose a benchmark to investigate models' logical reasoning capabilities in complex real-life scenarios.
Based on the multi-hop chain of reasoning, the explanation form includes three main components.
We evaluate the current best models' performance on this new explanation form.
arXiv Detail & Related papers (2022-10-22T16:01:13Z) - 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) - Logical Credal Networks [87.25387518070411]
This paper introduces Logical Credal Networks, an expressive probabilistic logic that generalizes many prior models that combine logic and probability.
We investigate its performance on maximum a posteriori inference tasks, including solving Mastermind games with uncertainty and detecting credit card fraud.
arXiv Detail & Related papers (2021-09-25T00:00:47Z) - 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) - From Checking to Inference: Actual Causality Computations as
Optimization Problems [79.87179017975235]
We present a novel approach to formulate different notions of causal reasoning, over binary acyclic models, as optimization problems.
We show that both notions are efficiently automated. Using models with more than $8000$ variables, checking is computed in a matter of seconds, with MaxSAT outperforming ILP in many cases.
arXiv Detail & Related papers (2020-06-05T10:56:52Z)
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.