Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Obligations and permissions on selfextensional logics

Andrea De Domenico, Ali Farjami, Krishna Manoorkar, Alessandra Palmigiano, Mattia Panettiere, Xiaolong Wang

TL;DR

The paper generalizes input/output logic to selfextensional logics, providing a principled framework for normative and permission reasoning beyond classical propositional logic. It defines and analyzes four permission schemes—negative, dual negative, static positive, and dynamic positive—within selfextensional settings, using closures and coherence notions to ensure robust interaction with normative systems. Core contributions include extending normative systems to selfextensional logics, formalizing generalized permission notions, and detailing their closure properties (and cross-coherence) with IO outputs; it also links these syntactic rules to modal and duality-based semantic characterizations. The work broadens the applicability of IO logic to a wide range of nonclassical logics, supporting normative reasoning in constructive, paraconsistent, and resource-sensitive contexts, with potential semantic and temporal extensions via subordination algebras and related dualities.

Abstract

We further develop the abstract algebraic logic approach to input/output logic initiated in \cite{wollic22}, where the family of selfextensional logics was proposed as a general background environment for input/output logics. In this paper, we introduce and discuss the generalizations of several types of permission (negative, dual negative, static, dynamic), as well as their interactions with normative systems, to various families of selfextensional logics, thereby proposing a systematic approach to the definition of normative and permission systems on nonclassical propositional bases.

Obligations and permissions on selfextensional logics

TL;DR

The paper generalizes input/output logic to selfextensional logics, providing a principled framework for normative and permission reasoning beyond classical propositional logic. It defines and analyzes four permission schemes—negative, dual negative, static positive, and dynamic positive—within selfextensional settings, using closures and coherence notions to ensure robust interaction with normative systems. Core contributions include extending normative systems to selfextensional logics, formalizing generalized permission notions, and detailing their closure properties (and cross-coherence) with IO outputs; it also links these syntactic rules to modal and duality-based semantic characterizations. The work broadens the applicability of IO logic to a wide range of nonclassical logics, supporting normative reasoning in constructive, paraconsistent, and resource-sensitive contexts, with potential semantic and temporal extensions via subordination algebras and related dualities.

Abstract

We further develop the abstract algebraic logic approach to input/output logic initiated in \cite{wollic22}, where the family of selfextensional logics was proposed as a general background environment for input/output logics. In this paper, we introduce and discuss the generalizations of several types of permission (negative, dual negative, static, dynamic), as well as their interactions with normative systems, to various families of selfextensional logics, thereby proposing a systematic approach to the definition of normative and permission systems on nonclassical propositional bases.
Paper Structure (23 sections, 19 theorems, 10 equations, 2 tables)

This paper contains 23 sections, 19 theorems, 10 equations, 2 tables.

Table of Contents

  1. Introduction
  2. Structure of the paper.
  3. Preliminaries
  4. Selfextensional logics and metalogical properties
  5. Logics as consequence relations.
  6. Consequence relations and closure operators.
  7. Metalogical properties.
  8. Normative systems
  9. Permission systems
  10. Negative permission systems.
  11. Static positive permission systems.
  12. Dynamic permission systems.
  13. Normative systems on selfextensional logics
  14. Permission systems on selfextensional logics
  15. Negative permission systems
  16. ...and 8 more sections

Key Result

Lemma 2.1

For any logic $\mathcal{L} = (\mathrm{Fm}, \vdash)$,

Theorems & Definitions (45)

  • Lemma 2.1
  • proof
  • Lemma 2.2
  • proof
  • Proposition 2.3
  • proof
  • Example 2.4
  • Remark 2.5
  • Proposition 2.6
  • proof
  • ...and 35 more