Epistemologische betrachtungen zu [S4, S5]

Lenzen, Wolfgang

doi:10.1007/bf00205012

Cited by 49 publications

(28 citation statements)

References 18 publications

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“…when the epistemic logic does not contain the 4 axiom. This complements Wolgang Lenzen's early work on epistemic-doxastic logics, in which knowledge is between S4 and S5 [14]. We offer a number of…”

supporting

confidence: 57%

“…On this view the belief operator in Stalnaker's system is a very strong variety of belief. Logically speaking, it is in fact close to what Lenzen calls "being convinced of" (überzeugt sein) [14]. Hence the thought arises that one could interpret that operator, and thereby the axiom SB, by using the notions of absolute certainty or even the mental component of knowledge.…”

Section: Basic Properties and Axiomatization Of The Belief Fragmentmentioning

confidence: 80%

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Knowledge, belief, normality, and introspection

2017

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We study two logics of knowledge and belief stemming from the work of Robert Stalnaker [18], omitting positive introspection for knowledge. The two systems are equivalent with positive introspection, but not without. We show that while the logic of beliefs remains unaffected by omitting introspection for knowledge in one system, it brings significant changes to the other. The resulting logic of belief is non-normal, and its complete axiomatization uses an infinite hierarchy of coherence constraints. We conclude by returning to the philosophical interpretation underlying both models of belief, showing that neither is strong enough to support a probabilistic interpretation, nor an interpretation in terms of certainty or the "mental component" of knowledge.

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supporting

confidence: 57%

Section: Basic Properties and Axiomatization Of The Belief Fragmentmentioning

confidence: 80%

Knowledge, belief, normality, and introspection

2017

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“…Dropping axiom 5 seems to be the most reasonable choice in light of the discussion about this axiom in Section 3.1. By dropping 5, we then only have to investigate the logics between S4 and S5 as possible candidates for a logic of knowledge (S5 excluded), as Lenzen did in (Lenzen, 1979 …”

Section: Principles Of Interaction With Strong Beliefmentioning

confidence: 99%

“…It has been proven that, for modal logic, explicit definability coincides with the conjunction of implicit definability and reducibility (unlike first-order logic, where the notion of explicit definability coincides with implicit definability only). In this paper, we are interested only in the notion of explicit definability, which is also used by Lenzen in (Lenzen, 1979). Here is its formal definition:…”

Section: Defining Knowledge In Terms Of Belief and Vice Versamentioning

confidence: 99%

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Principles of Knowledge, Belief and Conditional Belief

Aucher

2014

Logic, Argumentation &Amp; Reasoning

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International audienceWe review and examine in this paper the validity of the different axioms (and inference rules) of knowledge and belief and relating knowledge to belief which have been proposed in the epistemic !epistemic logic literature. In doing so, we encounter many of the problems that epistemic !epistemic logic has had to face in its relatively short (modern) history and provide relevant pointers for more details. We also contribute to this area by providing conditions under which the notion of belief can be formally defined in terms of knowledge , and vice versa. We also prove that certain convoluted axioms dealing only with the notion of knowledge can be derived from understandable interaction axioms relating knowledge and conditional belief

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Beschränkte und Unbeschränkte Reduktion von Konjunktionen von Modalitäten in S4

Lenzen

1980

Mathematical Logic Qtrly

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Einige der bekannten Erweiterungen dcs niodallogischen Systems S4 entstehenbei Axiomatisierung im Stile von LEMMON [5] -durch Hinzunahme von Axiomen der Gestalt A p 2 Bp, andere dureh Axiome der Form A p 2 ( B p 3 Cp), noch andere durch solche der Gestalt A p 2 ( B p 3 ( C p 2 Dp)), wobei A , B, C, D jeweils affirmative Modalitatenim Sinne beispielsweise von [4], S. 42 -sind.l) Fur eine einheitliehe Behandlung dieser Axiome und verwandter Prinzipien empfielt es sich, allgeniein ,,Konjunktionen" A, A . . . A .4, ( 7~ 2 1) von Modalitaten in Betraclit zu ziehen, wobei naturlicli fur jeden Satz p der Ausdruck A , A . . . A A,,(p) gleich der normalen n-fachen Konjunktion A l ( p ) A . . . A A,,@) sein s o l Den unbequemen Ausdruck ,,Ronjunktionen voii Modalitaten" kurzen wir durch ,,KM" ah, und beniitzen im Folgeiiden ,,K" (mit oder ohne Index) als metasprachliche Variable fur KM.Die Axiome der eingangs erwahnten S4-Erweiterungen sind also Einzelfalle des Schemas: K p 3 A p , bei dem A eine Modalitat und E; eine IiM darstellt. Da die Umkehrungen dieser Satze jeweils Theoreme von S4 sind, wird mit ihnen eine Reduktion der K M auf eine S4-Modalitat bewirkt. Es stellt sieh deshalb die Frage, ob nicht vielleicht samtliche Kalkule aus der recht anzahlstarken und unubersichtlichen Menge der S4-Erweiterungen durch bislang ununtersuchte KN-Reduktionen charakterisierbm sind, und ob umgekehrt solche Reduktionsprinzipien eventuell zur Entdcckung neuer Kalkule dcr genannten Familie fuhrcn. Beide Teilfragen sind negativ zu heantworten. Im ersten Teil dieser Arbeit wird sieh herausstellen, dal3 die Menge der durch (unbeschrankte) Reduktion beliebiger R M cliarakterisierharen Kalkule eine eehteund zwar relativ kleine -Teilmenge der Menge aller his dato bekannteii S4-Erweiterungen darstellt. I7nd diese Inklusion besteht sclbst d a m fort, wenn man zusatzlicli noch eine Reihe von Einschrankungen der KM-Reduktionsprinzipien in Betracht zieht, wie das in Teil 2 geschieht.

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Epistemologische betrachtungen zu [S4, S5]

Cited by 49 publications

References 18 publications

Knowledge, belief, normality, and introspection

Knowledge, belief, normality, and introspection

Principles of Knowledge, Belief and Conditional Belief

Beschränkte und Unbeschränkte Reduktion von Konjunktionen von Modalitäten in S4

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