A scheme for weakened negative introspection in autoepistemic reasoning

2005 ◽  
pp. 211-222 ◽  
Author(s):  
Tomi Janhunen ◽  
Ilkka Niemelä
Keyword(s):  
Negative Introspection

Evidence of Evidence in Epistemic Logic

2019 ◽  
pp. 265-297
Author(s):  
Timothy Williamson
Keyword(s):  
Epistemic Logic ◽  
Formal Models ◽  
Present Evidence ◽  
Negative Introspection ◽  
Bridge Principles

The slogan ‘Evidence of evidence is evidence’ is obscure. It has been applied to connect evidence in one situation to evidence in another. The link may be diachronic or interpersonal. Is present evidence of past or future evidence for p present evidence for p? Is evidence for me of evidence for you for p evidence for me for p? The chapter discusses intra-perspectival evidential links. Is present evidence for me of present evidence for me for p present evidence for me for p? Unless the connection holds between a perspective and itself, it is unlikely to hold between distinct perspectives. Evidence will be understood probabilistically, using formal models from epistemic logic. Bridge principles between first-level and higher-level epistemic conditions often imply versions of controversial principles, such as positive and negative introspection. Formalizations of intra-perspectival principles that evidence of evidence is evidence have similarly implausible connections.

Scholastická logika „vědění“ I.

2018 ◽  
Vol 15 (5) ◽  
pp. 127-205
Author(s):  
Miroslav Hanke ◽  
Keyword(s):  
Middle Ages ◽  
Epistemic Logic ◽  
Unified Framework ◽  
Founding Father ◽  
The Core ◽  
Cognitive Operations ◽  
Conceptual Background ◽  
John Wyclif ◽  
Negative Introspection ◽  
Positive Introspection

Fourteenth-century logic gave rise, among others, to the genre De scire et dubitare, which offered a unified framework for discussing different forms of epistemic sophisms by utilising the underlying systems of epistemic logic. One of the problems introduced in this context already by the founding father of this genre, William Heytesbury, was the so-called axiom of positive introspection, i.e., the principle that an agent who knows that something is the case, knows that she knows that it is the case. Owing to Heytesbury’s enormous popularity in the subsequent centuries, discussion of this problem became relatively widespread. This debate was addressed already in Boh’s seminal Epistemic Logic in the Later Middle Ages, which, despite its limitations acknowledged by its author, is a standard source. The present study elaborates on Boh by extending the corpus of his works (both in the sense of including new authors and of utilising manuscripts along with printed editions) and drawing new connections based on that. The core of the survey consists of an analysis of the positions of William Heytesbury and John Wyclif (both pertaining to the context of Merton College), their Italian reception by Peter of Mantua, and the “continental” reception of Heytesbury by John of Holland. The main goals of this study are to formalise the key arguments, which makes it possible to address the underlying systems of epistemic logic and their respective “strength”, and to articulate the conceptual background of those arguments and systems (the concepts of evidence, attention, and order of cognitive operations). The gist of the debate is, on one of the sides, an attempt to prove that it is impossible to doubt whether one knows that something is the case by employing whether the principles of positive introspection and of distribution of knowledge over implication, or the principles of positive and negative introspection combined.

scholarly journals Decidability for some justification logics with negative introspection

2013 ◽  
Vol 78 (2) ◽  
pp. 388-402 ◽  
Author(s):  
Thomas Studer
Keyword(s):  
Modal Logics ◽  
Model Construction ◽  
Negative Introspection ◽  
Novel Model ◽  
Finite Constant

AbstractJustification logics are modal logics that include justifications for the agent's knowledge. So far, there are no decidability results available for justification logics with negative introspection. In this paper, we develop a novel model construction for such logics and show that justification logics with negative introspection are decidable for finite constant specifications.

On the logic and role of Negative Introspection of Common Belief

1998 ◽  
Vol 35 (1) ◽  
pp. 17-36 ◽  
Author(s):  
Giacomo Bonanno ◽  
Klaus Nehring
Keyword(s):  
Common Belief ◽  
Negative Introspection

Concluding Remarks

2021 ◽  
pp. 264-268
Author(s):  
Sven Rosenkranz
Keyword(s):  
Epistemic Justification ◽  
Propositional Justification ◽  
Doxastic Justification ◽  
Negative Introspection

According to the account of epistemic justification developed in this book, one has propositional justification for p just in case one is in no position to know that one is in no position to know p; and one has doxastic justification for p just in case one is in no position to know that one does not know p. The account gives internalists much of what they want from a theory of justification—in particular, a notion of justification according to which propositional justification is non-factive and luminous, underwrites principles of positive and negative introspection, and remains available to the victims of systematic deception. All the while, that notion is explained in terms of other notions that clearly belong to the knowledge-firsters’ toolkit, and coheres with an externalist account of the grounds for justification.

scholarly journals SMALL INFINITARY EPISTEMIC LOGICS

2019 ◽  
Vol 12 (4) ◽  
pp. 702-735
Author(s):  
TAI-WEI HU ◽  
MAMORU KANEKO ◽  
NOBU-YUKI SUZUKI
Keyword(s):  
Game Theory ◽  
Common Knowledge ◽  
Expressive Power ◽  
Infinite Regress ◽  
Deductive Inference ◽  
Countably Infinite ◽  
Negative Introspection ◽  
Positive Introspection

AbstractWe develop a series of small infinitary epistemic logics to study deductive inference involving intra-/interpersonal beliefs/knowledge such as common knowledge, common beliefs, and infinite regress of beliefs. Specifically, propositional epistemic logics GL (Lα) are presented for ordinal α up to a given αo (αo ≥ ω) so that GL(L0) is finitary KDn with n agents and GL(Lα) (α ≥ 1) allows conjunctions of certain countably infinite formulae. GL(Lα) is small in that the language is countable and can be constructive. The set of formulae Lα is increasing up to α = ω but stops at ω We present Kripke-completeness for GL(Lα) for each α ≤ ω, which is proved using the Rasiowa–Sikorski lemma and Tanaka–Ono lemma. GL(Lα) has a sufficient expressive power to discuss intra-/interpersonal beliefs with infinite lengths. As applications, we discuss the explicit definability of Axioms T (truthfulness), 4 (positive introspection), 5 (negative introspection), and of common knowledge in GL(Lα) Also, we discuss the rationalizability concept in game theory in our framework. We evaluate where these discussions are done in the series GL(Lα), α ≤ ω.

Group belief

2020 ◽  
Author(s):  
Thomas Ågotnes ◽  
Yì N Wáng
Keyword(s):  
Modal Logic ◽  
Common Belief ◽  
Distributed Knowledge ◽  
Common Assumption ◽  
Group Knowledge ◽  
Group Belief ◽  
The Common ◽  
Negative Introspection

Abstract While logical formalizations of group notions of knowledge such as common and distributed knowledge have received considerable attention in the literature, most approaches being based on modal logic, group notions of belief have received much less attention. In this paper we systematically study standard notions of group belief under different assumptions about the properties of belief. In particular, we map out (lack of) preservation of belief properties against different standard definitions of group belief. It turns out that what is called group belief most often is not actually belief, i.e. does not have the properties of belief. In fact, even what is called group knowledge is sometimes not actually knowledge either. For example, under the common assumption that belief has the KD45 properties, neither common belief (does not satisfy the negative introspection axiom 5) nor distributed belief (does not satisfy the consistency axiom D) are not actually belief. There has been some confusion in the literature regarding soundness of proposed axiomatizations of logics with distributed knowledge, related to the mentioned lack of preservation. In this paper we also present detailed completeness proofs of sound and complete axiomatizations of KD45 with distributed belief, both with and without common belief.

Note on unawareness: Negative Introspection versus AU Introspection (and KU Introspection)

2011 ◽  
Vol 41 (2) ◽  
pp. 325-329 ◽  
Author(s):  
Yi-Chun Chen ◽  
Jeffrey C. Ely ◽  
Xiao Luo
Keyword(s):  
Negative Introspection

scholarly journals Reasoning about Minimal Belief and Negation as Failure

1999 ◽  
Vol 11 ◽  
pp. 277-300 ◽  
Author(s):  
R. Rosati
Keyword(s):  
Logic Programming ◽  
Nonmonotonic Reasoning ◽  
Default Logic ◽  
Polynomial Hierarchy ◽  
Autoepistemic Logic ◽  
The Third ◽  
Negation As Failure ◽  
Negative Introspection

We investigate the problem of reasoning in the propositional fragment of MBNF, the logic of minimal belief and negation as failure introduced by Lifschitz, which can be considered as a unifying framework for several nonmonotonic formalisms, including default logic, autoepistemic logic, circumscription, epistemic queries, and logic programming. We characterize the complexity and provide algorithms for reasoning in propositional MBNF. In particular, we show that entailment in propositional MBNF lies at the third level of the polynomial hierarchy, hence it is harder than reasoning in all the above mentioned propositional formalisms for nonmonotonic reasoning. We also prove the exact correspondence between negation as failure in MBNF and negative introspection in Moore's autoepistemic logic.

Outline of a theory of justification

2021 ◽  
pp. 1-17
Author(s):  
Sven Rosenkranz
Keyword(s):  
Modal Logic ◽  
Epistemic Possibility ◽  
The Novel ◽  
Metaphysical Possibility ◽  
Propositional Justification ◽  
Normal Modal Logic ◽  
Present Account ◽  
Internal Condition ◽  
The Difference ◽  
Negative Introspection

Core theses of the novel account of justification to be developed are first stated: one has propositional justification for p just in case one is in no position to know that one is in no position to know p; and one has doxastic justification for p just in case one is in no position to know that one does not know p. Unlike other theories that conceive of justification in terms of the metaphysical possibility of knowing, the present account thus construes it as a distinctive kind of epistemic possibility. It treats propositional justification as non-factive, both its presence and its absence as luminous conditions, and by assuming a weak non-normal modal logic for knowledge and being in a position to know, validates principles of positive and negative introspection for it. The account thereby attributes features to justification that internalists care about. But it does so without construing justification as an internal condition. The account allows one to systematically distinguish between the condition of being justified and the metaphysical grounds for its obtaining, thereby heeding externalist insights into the difference between the good cases and the bad cases envisaged by radical scepticism. Lines of argument that show the account’s potential, e.g. in dealing with the preface and lottery paradoxes, are previewed, and so are lines of defence against challenges and objections, including prominent anti-luminosity arguments.

Sign in / Sign up

Export Citation Format

Share Document