scholarly journals Reasoning About Prescription and Description Using Prioritized Default Rules

10.29007/swdn ◽  
2018 ◽  
Author(s):  
Valentin Cassano ◽  
Carlos Areces ◽  
Pablo Castro
Keyword(s):  
Software Engineering ◽  
Deontic Logic ◽  
Default Logic ◽  
Logical Framework ◽  
Standard Deontic Logic ◽  
Default Rules

In this paper we introduce a prioritized default logic. We build this logic modularly from Standard Deontic Logic by the addition of default rules and priorities among them. Our main aim is to provide a logical framework to reason about scenarios where prescriptive and descriptive statements coexist and may be incomplete and contradictory. We motivate and illustrate the technical elements of our work with the use of examples (classical, and coming from software engineering). In addition, we present sound, complete, and terminating (with loop check) tableau-based proof calculi for credulous and sceptical reasoning in our logic.

scholarly journals Two dimensional Standard Deontic Logic [including a detailed analysis of the 1985 Jones–Pörn deontic logic system]

Synthese ◽  
2011 ◽  
Vol 187 (2) ◽  
pp. 623-660 ◽  
Author(s):  
Mathijs de Boer ◽  
Dov M. Gabbay ◽  
Xavier Parent ◽  
Marija Slavkovic
Keyword(s):  
Detailed Analysis ◽  
Deontic Logic ◽  
Two Dimensional ◽  
Standard Deontic Logic ◽  
Logic System

Constrained Epistemic Extension on Agent Knowledge Acquisition

2013 ◽  
Vol 651 ◽  
pp. 943-948
Author(s):  
Zhi Ling Hong ◽  
Mei Hong Wu
Keyword(s):  
Epistemic Logic ◽  
Information Acquisition ◽  
Default Logic ◽  
Dynamic Epistemic Logic ◽  
Default Reasoning ◽  
Multi Agent Systems ◽  
Negotiation Strategy ◽  
Agent Systems ◽  
Multi Agent ◽  
Default Rules

In multi-agent systems, a number of autonomous pieces of software (the agents) interact in order to execute complex tasks. This paper proposes a logic framework portrays agent’s communication protocols in the multi-agent systems and a dynamic negotiation model based on epistemic default logic was introduced in this framework. In this paper, we use the constrained default rules to investigate the extension of dynamic epistemic logic, and constrained epistemic extension construct an efficient negotiation strategy via constrained epistemic default reasoning, which guarantees the important natures of extension existence and semi-monotonicity. We also specify characteristic of the dynamic updating when agent learn new knowledge in the logical framework. The method for the information sharing signify the usefulness of logical tools carried out in the dynamic process of information acquisition, and the distributed intelligent information processing show the effectiveness of reasoning default logic in the dynamic epistemic logic theory.

Omega-inconsistency without cuts and nonstandard models

2016 ◽  
Vol 13 (5) ◽  
Author(s):  
Andreas Fjellstad
Keyword(s):  
Deontic Logic ◽  
Sequent Calculus ◽  
Standard Deontic Logic ◽  
Nonstandard Models ◽  
Deontic Modality ◽  
The Relationship ◽  
Labelled Sequent Calculus ◽  
Models Of Arithmetic

This paper concerns the relationship between transitivity of entailment, omega-inconsistency and nonstandard models of arithmetic. First, it provides a cut-free sequent calculus for non-transitive logic of truth STT based on Robinson Arithmetic and shows that this logic is omega-inconsistent. It then identifies the conditions in McGee (1985) for an omega-inconsistent logic as quantified standard deontic logic, presents a cut-free labelled sequent calculus for quantified standard deontic logic based on Robinson Arithmetic where the deontic modality is treated as a predicate, proves omega-inconsistency and shows thus, pace Cobreros et al.(2013), that the result in McGee (1985) does not rely on transitivity. Finally, it also explains why the omega-inconsistent logics of truth in question do not require nonstandard models of arithmetic.

scholarly journals Reactive standard deontic logic

2012 ◽  
Vol 25 (1) ◽  
pp. 117-157 ◽  
Author(s):  
D. M. Gabbay ◽  
C. Strasser
Keyword(s):  
Deontic Logic ◽  
Standard Deontic Logic

The Geometry of Standard Deontic Logic

2009 ◽  
Vol 3 (1) ◽  
pp. 19-57 ◽  
Author(s):  
Alessio Moretti
Keyword(s):  
Deontic Logic ◽  
Standard Deontic Logic

scholarly journals The Complexity of Circumscription in DLs

2009 ◽  
Vol 35 ◽  
pp. 717-773 ◽  
Author(s):  
P. A. Bonatti ◽  
C. Lutz ◽  
F. Wolter
Keyword(s):  
Description Logics ◽  
Default Logic ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Alternative Approach ◽  
Default Rules ◽  
Logic Description ◽  
Interesting Alternative ◽  
Natural Way

As fragments of first-order logic, Description logics (DLs) do not provide nonmonotonic features such as defeasible inheritance and default rules. Since many applications would benefit from the availability of such features, several families of nonmonotonic DLs have been developed that are mostly based on default logic and autoepistemic logic. In this paper, we consider circumscription as an interesting alternative approach to nonmonotonic DLs that, in particular, supports defeasible inheritance in a natural way. We study DLs extended with circumscription under different language restrictions and under different constraints on the sets of minimized, fixed, and varying predicates, and pinpoint the exact computational complexity of reasoning for DLs ranging from ALC to ALCIO and ALCQO. When the minimized and fixed predicates include only concept names but no role names, then reasoning is complete for NExpTime^NP. It becomes complete for NP^NExpTime when the number of minimized and fixed predicates is bounded by a constant. If roles can be minimized or fixed, then complexity ranges from NExpTime^NP to undecidability.

scholarly journals STATISTICAL INFERENCE AS DEFAULT REASONING

1999 ◽  
Vol 13 (02) ◽  
pp. 267-283 ◽  
Author(s):  
HENRY E. KYBURG ◽  
CHOH MAN TENG
Keyword(s):  
Statistical Inference ◽  
Statistical Test ◽  
Default Logic ◽  
Default Reasoning ◽  
Default Rules

Classical statistical inference is nonmonotonic in nature. We show how it can be formalized in the default logic framework. The structure of statistical inference is the same as that represented by default rules. In particular, the prerequisite corresponds to the sample statistics, the justifications require that we do not have any reason to believe that the sample is misleading, and the consequence corresponds to the conclusion sanctioned by the statistical test.

scholarly journals Complexity of Prioritized Default Logics

1998 ◽  
Vol 9 ◽  
pp. 423-461 ◽  
Author(s):  
J. Rintanen
Keyword(s):  
Computational Complexity ◽  
Default Logic ◽  
Default Reasoning ◽  
Polynomial Hierarchy ◽  
Inference Mechanism ◽  
Default Rules ◽  
Computational Properties ◽  
Default Logics

In default reasoning, usually not all possible ways of resolving conflicts between default rules are acceptable. Criteria expressing acceptable ways of resolving the conflicts may be hardwired in the inference mechanism, for example specificity in inheritance reasoning can be handled this way, or they may be given abstractly as an ordering on the default rules. In this article we investigate formalizations of the latter approach in Reiter's default logic. Our goal is to analyze and compare the computational properties of three such formalizations in terms of their computational complexity: the prioritized default logics of Baader and Hollunder, and Brewka, and a prioritized default logic that is based on lexicographic comparison. The analysis locates the propositional variants of these logics on the second and third levels of the polynomial hierarchy, and identifies the boundary between tractable and intractable inference for restricted classes of prioritized default theories.

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