Wyniki wyszukiwania - Biblioteka Nauki

1

Fibring Epistemic and Temporal Logics

100%

Krawczyk K. A.

Logic and Logical Philosophy

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2019

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tom 28

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nr 1

195-199

EN

Book Reviews: Dariusz Surowik, Logika, wiedza i czas. Problemy i metody temporalno-logicznej reprezentacji wiedzy (Logic, Knowledge and Time. Problems and Methods of Temporal-Logical Representation of Knowledge), Wydawnictwo Uniwersytetu w Białymstoku, Białystok 2013, 357 pages, ISBN 978-83-7431-375-9.

2

Erotetic Epistemic Logic

80%

Peliš M.

Logic and Logical Philosophy

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2017

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tom 26

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nr 3 Special Issue on Question Processing. Guest Editors: Mariusz Urbański, Michiel van Lambalgen, and Marcin Koszowy

357–381

EN

This paper presents a logic of questions developed as an extension of (S5) epistemic logic. We discuss many features that are important for erotetic logic (formalization and semantics of questions, answerhood conditions, and inferential structures with questions). The aim is to introduce an erotetic system which corresponds well with epistemic terms and can form an appropriate background for dynamic approaches in epistemic logic.

3

Dynamic Epistemic Logic and Logical Omniscience

80%

Rasmussen M. S.

Logic and Logical Philosophy

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2015

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tom 24

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nr 3

377–399

EN

Epistemic logics based on the possible worlds semantics suffer from the problem of logical omniscience, whereby agents are described as knowing all logical consequences of what they know, including all tautologies. This problem is doubly challenging: on the one hand, agents should be treated as logically non-omniscient, and on the other hand, as moderately logically competent. Many responses to logical omniscience fail to meet this double challenge because the concepts of knowledge and reasoning are not properly separated. In this paper, I present a dynamic logic of knowledge that models an agent’s epistemic state as it evolves over the course of reasoning. I show that the logic does not sacrifice logical competence on the altar of logical non-omniscience.

4

Logic of Algorithmic Knowledge

80%

Surowik D.

Studies in Logic, Grammar and Rhetoric

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2015

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tom 42

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nr 1

163-172

EN

In this paper we consider the construction of a LAK system of temporal-epistemic logic which is used to formally describe algorithmic knowledge. We propose an axiom system of LAK and discuss the basic properties of this logic.

5

A Reconstruction of Default Conditionals within Epistemic Logic

80%

Koutras C. D. , Moyzes C. , Rantsoudis C.

Fundamenta Informaticae

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2019

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tom Vol. 166, nr 2

167--197

EN

Default conditionals are statements that express a condition of normality, in the form ‘if φ then normally ψ’ and are of primary importance in Knowledge Representation. There exist modal approaches to the construction of conditional logics of normality. Most of them are built on notions of preference among possible worlds, corresponding to the semantic intuition that φ ⇒ ψ is true in a situation if in the most preferred (most ‘normal’) situations in which φ is true, ψ is also true. It has been noticed that there exist natural epistemic readings of a default conditional, but this direction has not been thoroughly explored. A statement of the form ‘something known to be a bird, that can be consistently believed to fly, does fly’ involves well-known epistemic attitudes and allows the possibility of defining defaults within the rich framework of Epistemic Logic. We pursue this direction here and proceed to define conditionals within KBE, a recently introduced S4.2-based modal logic of knowledge, belief and estimation. In this logic, knowledge is a normal S4 operator, belief is a normal KD45 operator and estimation is a non-normal operator interpreted as a ‘majority’ quantifier over the set of epistemically alternative situations. We define and explore various conditionals using the epistemic operators of KBE, capturing φ ⇒ ψ in various ways, including ‘according to the agent’s knowledge, an estimation that φ is true implies the estimation that (φ∧ψ) is true’ or ‘if φ is known and there is no reason to believe ¬ψ then ψ can be plausibly inferred’. Overall, we define here three nonmonotonic default conditionals, one conditional satisfying monotonicity (strengthening the antecedent) and two nonmonotonic conditionals that do not satisfy the ubiquitous axiom ID (reflexivity). Our project provides concrete evidence that the machinery of epistemic logic can be exploited for the study of default conditionals.

6

A Tractable Rule Language in the Modal and Description Logic that Combines CPDL with Regular Grammar Logic

70%

Nguyen L. A.

Fundamenta Informaticae

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2016

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tom Vol. 143, nr 1/2

113--139

EN

Combining CPDL (Propositional Dynamic Logic with Converse) and regular grammar logic results in an expressive modal logic denoted by CPDLreg. This logic covers TEAMLOG, a logical formalism used to express properties of agents’ cooperation in terms of beliefs, goals and intentions. It can also be used as a description logic for expressing terminological knowledge, in which both regular role inclusion axioms and CPDL-like role constructors are allowed. In this paper, we develop an expressive and tractable rule language called Horn-CPDLreg. As a special property, this rule language allows the concept constructor “universal restriction” to appear on the left hand side of general concept inclusion axioms. We use a special semantics for Horn-CPDLreg that is based on pseudo-interpretations. It is called the constructive semantics and coincides with the traditional semantics when the concept constructor “universal restriction” is disallowed on the left hand side of concept inclusion axioms or when the language is used as an epistemic formalism and the accessibility relations are serial. We provide an algorithm with PTIME data complexity for checking whether a knowledge base in Horn-CPDLreg has a pseudo-model. This shows that the instance checking problem in Horn-CPDLreg with respect to the constructive semantics has PTIME data complexity.

7

Consistency-based Revision of Structured Belief Bases

70%

Korpusik M. , Łukaszewicz W. , Madalińska-Bugaj E.

Fundamenta Informaticae

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2015

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tom Vol. 136, nr 4

381--404

EN

In this paper we extend a consistency-based approach (originally introduced by Delgrande and Schaub) to belief revision for structured belief bases. We explicitly distinguish between observations, i.e., facts that an epistemic agent observes or is being told, and rules representing general knowledge about the considered world. When new information becomes available respective sets are being altered in a different way to preserve parts of knowledge during the revision process. Such an approach allows us to deal with difficult and complex scenarios, involving defeasible information and derivation filtering, with common-sense results.

8

Explicitní/implicitní přesvědčení a derivační systémy

70%

Raclavský J. , Pezlar I.

Filosofický časopis (Philosophical Journal)

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2019

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tom 67

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nr 1

89-120

EN

The problem of hyperintensional contexts, and the problem of logical omniscience, shows the severe limitation of possible-worlds semantics which is employed also in standard epistemic logic. As a solution, we deploy here hyperintensional semantics according to which the meaning of an expression is an abstract structured algorithm, namely Tichý’s construction. Constructions determine the denotata of expressions. Propositional attitudes are modelled as attitudes towards constructions of truth values. Such a model of belief is, of course, inferentially restrictive. We therefore also propose a model of implicit knowledge, which is the collection of a possible agent’s explicit beliefs which are related through a derivation system mastered by the agent. A derivation system consists of beliefs and derivation rules by means of which the agent may derive beliefs different from the beliefs she is actually related to. Conditions imposed on the set of base beliefs and the set of rules capture the limitations of the agent’s deriving capabilities.

DE

Das Problem hyperintensionaler Zusammenhänge bzw. das Problem der logischen Allwissenheit verweist auf die erhebliche Einschränkung der Semantik der möglichen Welten, die auch von der herkömmlichen epistemischen Logik akzeptiert wird. Als Lösung verwenden wir hier die hyperintensionale Semantik, der gemäß die Bedeutung eines Ausdrucks ein abstrakter strukturierter Algorithmus ist, namentlich die sog. Konstruktion Pavel Tichýs. Die Konstruktionen bestimmen die Begriffsreferenten. Die sog. propositionalen Einstellungen sind daher in dem von uns verfolgtem Ansatz keine Einstellungen im Bezug auf Propositionen, sondern im Bezug auf Konstruktionen von Wahrheitswerten. Dieses Modell der expliziten Überzeugung ist inferentiell restriktiv, weshalb wir hier das Modell einer impliziten Überzeugung vorschlagen. Dieses Modell wird als Komplex expliziter Einstellungen eines Agenten zu verschiedenen Konstruktionen von Wahrheitswerten erläutert, die durch das vom Agenten beherrschte abgeleitete System miteinander verbunden werden. Das abgeleitete System besteht vor allem aus Objekten der Überzeugung und aus Ableitungsregeln, mit deren Hilfe der Agent die Konsequenzen seiner Überzeugungen ableiten kann; eine solche Überzeugung wird als abgeleitet bezeichnet. Die Menge der Überzeugungen und die Menge der Ableitungsregeln unterliegen dabei Bedingungen, die die Einschränkungen der kognitiven Fähigkeit des Agenten erfassen.

9

Proof theory of epistemic logic of programs

70%

Maffezioli P. , Naibo A.

Logic and Logical Philosophy

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2014

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tom 23

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nr 3

301–328

EN

A combination of epistemic logic and dynamic logic of programs is presented. Although rich enough to formalize some simple game-theoretic scenarios, its axiomatization is problematic as it leads to the paradoxical conclusion that agents are omniscient. A cut-free labelled Gentzen-style proof system is then introduced where knowledge and action, as well as their combinations, are formulated as rules of inference, rather than axioms. This provides a logical framework for reasoning about games in a modular and systematic way, and to give a step-by-step reconstruction of agents omniscience. In particular, its semantic assumptions are made explicit and a possible solution can be found in weakening the properties of the knowledge operator.

10

Once More about Moore’s Paradox in Epistemic Logic and Belief Change Theory

60%

LECHNIAK M.

Roczniki Filozoficzne

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2018

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tom 66

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nr 3

77-99

EN

In this article, it was first presented Moore’s paradox per se and after the author focused on the logical perspective—at first he analyzed these considerations in the field of so-called standard epistemic logic and after on the formal theory of belief change.

PL

W niniejszym artykule najpierw został zaprezentowany paradoks Moore’a per se, a następnie autor skupił się na perspektywie logicznej,analizując wpierw problem w zakresie tak zwanej standardowej logiki epistemicznej, a potem formalnej teorii zmian przekonaniowych.

11

On notions of assertion, knowledge and opinion in epistemic logic

60%

Nieznański E.

Studia Philosophiae Christianae

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2011

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tom 47

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nr 4

73-83

EN

In the article there is presented a formalized theory in frame of which there are compared three stages of convictions (S – I am (firmly) convinced, D – I admit, P - I suppose), W operator understood as “I know, that” and M operator reads as “I believe, that”. The theory is characterized both on syntactic and semantic level. In frame of a syntactic description there are noticed certain logical square connections between S and D, e.g.: S(p) is contrary to D(Np) and S(p) is opposite to S(Np). S(Np) is contrary to D(p). Expressions: D(p) and D(Np) are sub-opposite. Operators P and S are introduced axiomatically. Operators D, W, and M are characterized by definitions, which are understood in the following way: Def 1: I admit, that p iff I am not firmly convinced, that not–p Def 2: I know, that p iff p and I am firmly convinced, that p Def 3: I believe, that p iff I suppose that p and I admit, that not–p. On semantic level we consider a structure (T, <, ≤ ), where T is a set of time points, < is a relation of being earlier than, and ≤ is a relation of being not later than.

PL

W artykule przedstawiono propozycję sformalizowanej teorii, w której nadane oraz wzajemnie porównywane są znaczenia trzech stopni przekonań (S- sądzę stanowczo, D- dopuszczam, P- przypuszczam), funktora W rozumianego jako zwrot „wiem, że” oraz funktora M rozumianego jako zwrot „mniemam, że”. Teoria ta posiada zarówno ujęcie składniowe jak i semantyczne. Przedstawiając ujęcie składniowe tworzonej teorii zwraca się uwagę na to, że pomiędzy funktorem S oraz D zachodzą związki kwadratu logicznego. Oznacza to, że S(p) jest sprzeczne z D(Np), natomiast przeciwne do S(Np). S(Np) jest sprzeczne z D(p). Parę wyrażeń podprzeciwnych stanowią: D(p) oraz D(Np). Pojęcia: „sądzę stanowczo”, „przypuszczam”, „dopuszczam” wyrażają różne stopnie przekonania. Najmocniejszy stopień przekonania kryje się w zwrocie „sądzę stanowczo”, słabszy w zwrocie „przypuszczam”, a najsłabszy w zwrocie „dopuszczam”. Dlatego też z S(p) wynika logicznie P(p), a z P(p) wynika logicznie D(p). Funktor P jak i S wprowadzone są do teorii aksjomatycznie. Funktory: D (dopuszczam, że),W (wiem, że) oraz funktor M (mniemam, że) wprowadzone są poprzez kontekstowe definicje równościowe. Definicje te w przełożeniu na język naturalny brzmią następująco: Def 1: Dopuszczam, że p wtedy i tylko wtedy, gdy nie sądzę stanowczo, iż nieprawda, że p. Def 2: Wiem, że p wtedy i tylko wtedy, gdy zarazem p oraz sądzę stanowczo, że p. Def 3: Mniemam, że p wtedy i tylko wtedy, gdy przypuszczam, że p, ale jednocześnie dopuszczam, że nieprawda, że p. Zgodnie z definicją Def 2 funktor wiedzy jest silniejszy od każdego z rozpatrywanych stopni przekonań. W ujęciu semantycznym została wyróżniona struktura (T, <, ≤ ) – w której T jest zbiorem punktów czasowych, < to relacja bycia wcześniejszym, natomiast ≤ jest relacją bycia nie późniejszym – i zdefiniowane indukcyjnie pojęcie prawdziwości w chwili t.

12

Knowability as De Re Modality: A Certain Solution to Fitch Paradox

31%

Jarmużek T. , Krawczyk K. , Palczewski R.

Roczniki Filozoficzne

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2020

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tom 68

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nr 4

291-313

EN

In the paper, we try to find a new, intuitive solution to the Fitch paradox. We claim that traditional expression of Knowability Principle (p → ◊Kp) is based on erroneous understanding of knowability as de dicto modality. Instead, we propose to understand knowability as de re modality. In the paper we present the minimal logic of knowability in which Knowability Principle is valid, but Fitch Paradox does not hold anymore. We characterize the logic semantically as well as by an axiomatic and tableaux procedure approach.

PL

Poznawalność jako modalność de re: pewne rozwiązanie paradoksu Fitcha W artykule staramy się znaleźć nowe, intuicyjne rozwiązanie paradoksu Fitcha. Twierdzimy, że tradycyjne wyrażenie zasady poznawalności (p → ◊Kp) opiera się na błędnym rozumieniu poznawalności jako modalności de dicto. Zamiast tego proponujemy rozumieć poznawalność jako modalność de re. W artykule przedstawiamy minimalną logikę poznawalności, w której zasada poznawalności jest ważna, ale paradoks Fitcha już nie obowiązuje. Logikę charakteryzujemy semantycznie, a także poprzez podejście aksjomatyczne i tabelaryczne.