A Preference-Based Approach to Defeasible Deontic Inference

2020 ◽  
Author(s):  
James Delgrande
Keyword(s):  
Propositional Logic ◽  
Polynomial Hierarchy ◽  
Deontic Reasoning ◽  
Desirable Outcome ◽  
Interesting Difference ◽  
Completeness Result ◽  
Syntactic Approach ◽  
Soundness And Completeness

In this paper we present an approach to defeasible deontic inference. Given a set of rules R expressing conditional obligations and a formula A giving contingent information, the goal is to determine the most desirable outcome with respect to this information. Semantically, the rules R induce a partial preorder on the set of models, giving the relative desirability of each model. Then the set of minimal A models characterises the best that can be attained given that A holds. A syntactic approach is also given, in terms of maximal subsets of material counterparts of rules in R, and that yields a formula that expresses the best outcome possible given that A holds. These approaches are shown to coincide, providing an analogue to a soundness and completeness result. Complexity is not unreasonable, being at the second level of the polynomial hierarchy when the underlying logic is propositional logic. The approach yields desirable and intuitive results, including for the various “paradoxes” of deontic reasoning. The approach also highlights an interesting difference in how specificity is dealt with in nonmonotonic and deontic reasoning.

scholarly journals Deduction in Non-Fregean Propositional Logic SCI

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 115 ◽  
Author(s):  
Joanna Golińska-Pilarek ◽  
Magdalena Welle
Keyword(s):  
Propositional Logic ◽  
Sequent Calculus ◽  
Classical Propositional Logic ◽  
Tableau System ◽  
Soundness And Completeness

We study deduction systems for the weakest, extensional and two-valued non-Fregean propositional logic SCI . The language of SCI is obtained by expanding the language of classical propositional logic with a new binary connective ≡ that expresses the identity of two statements; that is, it connects two statements and forms a new one, which is true whenever the semantic correlates of the arguments are the same. On the formal side, SCI is an extension of classical propositional logic with axioms characterizing the identity connective, postulating that identity must be an equivalence and obey an extensionality principle. First, we present and discuss two types of systems for SCI known from the literature, namely sequent calculus and a dual tableau-like system. Then, we present a new dual tableau system for SCI and prove its soundness and completeness. Finally, we discuss and compare the systems presented in the paper.

Update Semantics in Communicated Information System

2011 ◽  
Vol 403-408 ◽  
pp. 1460-1465
Author(s):  
Guang Ming Chen ◽  
Xiao Wu Li
Keyword(s):  
Information Systems ◽  
Propositional Logic ◽  
General Purpose ◽  
Main Task ◽  
Information Communication ◽  
Classical Propositional Logic ◽  
Update Semantics ◽  
Essential Form ◽  
Soundness And Completeness ◽  
Multi Agents

An approach, which is called Communicated Information Systems, is introduced to describe the information available in a number of agents and specify the information communication among the agents. The systems are extensions of classical propositional logic in multi-agents context, providing with us a way by which not only the agent’s own information, but the information from other agents may be applied to agent’s reasoning as well. Communication rules, which are defined in the most essential form, can be regarded as the base to characterize some interesting cognitive proporties of agents. Since the corresponding communication rules can be chosen for different applications, the approach is general purpose one. The other main task is that the soundness and completeness of the Communicated Information Systems for the update semantics have been proved in the paper.

scholarly journals Hybrid Deduction–Refutation Systems

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 118 ◽  
Author(s):  
Valentin Goranko
Keyword(s):  
Propositional Logic ◽  
Proof Theory ◽  
Natural Deduction ◽  
Basic Theory ◽  
Logical System ◽  
Classical Propositional Logic ◽  
Deductive Systems ◽  
Refutation Systems ◽  
Soundness And Completeness

Hybrid deduction–refutation systems are deductive systems intended to derive both valid and non-valid, i.e., semantically refutable, formulae of a given logical system, by employing together separate derivability operators for each of these and combining ‘hybrid derivation rules’ that involve both deduction and refutation. The goal of this paper is to develop a basic theory and ‘meta-proof’ theory of hybrid deduction–refutation systems. I then illustrate the concept on a hybrid derivation system of natural deduction for classical propositional logic, for which I show soundness and completeness for both deductions and refutations.

scholarly journals Logics for Knowability

2021 ◽  
pp. 1-42
Author(s):  
Mo Liu ◽  
Jie Fan ◽  
Hans Van Ditmarsch ◽  
Louwe B. Kuijer
Keyword(s):  
Propositional Logic ◽  
Single Agent ◽  
Classical Propositional Logic ◽  
Public Announcement ◽  
Public Announcement Logic ◽  
Multi Agent ◽  
Soundness And Completeness

In this paper, we propose three knowability logics LK, LK−, and LK=. In the single-agent case, LK is equally expressive as arbitrary public announcement logic APAL and public announcement logic PAL, whereas in the multi-agent case, LK is more expressive than PAL. In contrast, both LK− and LK= are equally expressive as classical propositional logic PL. We present the axiomatizations of the three knowability logics and show their soundness and completeness. We show that all three knowability logics possess the properties of Church-Rosser and McKinsey. Although LK is undecidable when at least three agents are involved, LK− and LK= are both decidable.

scholarly journals From Hilbert proofs to consecutions and back

2021 ◽  
Vol 18 (2) ◽  
Author(s):  
Tore Fjetland Øgaard
Keyword(s):  
Natural Deduction ◽  
Sequent Calculus ◽  
Substructural Logics ◽  
Structural Rules ◽  
Completeness Result ◽  
Soundness And Completeness

Restall set forth a "consecution" calculus in his An Introduction to Substructural Logics. This is a natural deduction type sequent calculus where the structural rules play an important role.  This paper looks at different ways of extending Restall's calculus. It is shown that Restall's weak soundness and completeness result with regards to a Hilbert calculus can be extended to a strong one so as to encompass what Restall calls proofs from assumptions. It is also shown how to extend the calculus so as to validate the metainferential rule of reasoning by cases, as well as certain theory-dependent rules.

A HENKIN-STYLE PROOF OF COMPLETENESS FOR FIRST-ORDER ALGEBRAIZABLE LOGICS

2015 ◽  
Vol 80 (1) ◽  
pp. 341-358 ◽  
Author(s):  
PETR CINTULA ◽  
CARLES NOGUERA
Keyword(s):  
Propositional Logic ◽  
Order Logic ◽  
First Order Logic ◽  
Algebraic Semantics ◽  
Subdirectly Irreducible ◽  
Algebraizable Logics ◽  
First Order ◽  
Completeness Result ◽  
Subdirectly Irreducible Algebras

AbstractThis paper considers Henkin’s proof of completeness of classical first-order logic and extends its scope to the realm of algebraizable logics in the sense of Blok and Pigozzi. Given a propositional logic L (for which we only need to assume that it has an algebraic semantics and a suitable disjunction) we axiomatize two natural first-order extensions L∀m and L∀ and prove that the former is complete with respect to all models over algebras from , while the latter is complete with respect to all models over relatively finitely subdirectly irreducible algebras. While the first completeness result is relatively straightforward, the second requires non-trivial modifications of Henkin’s proof by making use of the disjunction connective. As a byproduct, we also obtain a form of Skolemization provided that the algebraic semantics admits regular completions. The relatively modest assumptions on the propositional side allow for a wide generalization of previous approaches by Rasiowa, Sikorski, Hájek, Horn, and others and help to illuminate the “essentially first-order” steps in the classical Henkin’s proof.

Deontic Reasoning, Mental Models Theory and Traffic Signs Information

2007 ◽  
Author(s):  
Cristina Vargas ◽  
Sergio Moreno-Rios ◽  
Candida Castro ◽  
Geoffrey Underwood
Keyword(s):  
Mental Models ◽  
Traffic Signs ◽  
Deontic Reasoning ◽  
Mental Models Theory

Religion and Mythology in the Chilembwe Rising of 1915 in Nyasaland and the Easter Rising of 1916 in Ireland: Preparing for the End Times?

2017 ◽  
Vol 23 (1) ◽  
pp. 51-66
Author(s):  
T. Jack Thompson
Keyword(s):  
The United States ◽  
Religious Motivation ◽  
Easter Rising ◽  
British Rule ◽  
The People ◽  
Head Of State ◽  
Interesting Difference ◽  
Racial Injustice ◽  
Book Of Daniel ◽  
End Times

Superficially there are many parallels between the Chilembwe Rising of 1915 in Nyasaland and the Easter Rising of 1916 in Ireland – both were anti-colonial rebellions against British rule. One interesting difference, however, occurs in the way academics have treated John Chilembwe, leader of the Nyasaland Rising, and Patrick Pearse, one of the leaders of the Irish Rising and the man who was proclaimed head of state of the Provisional government of Ireland. For while much research on Pearse has dealt with his religious ideas, comparatively little on Chilembwe has looked in detail at his religious motivation – even though he was the leader of an independent church. This paper begins by looking at some of the major strands in the religious thinking of Pearse, before going on to concentrate on the people and ideas which influenced Chilembwe both in Nyasaland and the United States. It argues that while many of these ideas were initially influenced by radical evangelical thought in the area of racial injustice, Chilembwe's thinking in the months immediately preceding his rebellion became increasingly obsessed by the possibility that the End Time prophecies of the Book of Daniel might apply to the current political position in Nyasaland. The conclusion is that much more academic attention needs to be given to the millennial aspects of Chilembwe's thinking as a contributory motivation for rebellion.

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