Probabilistic extensions of various logical systems

Probabilistic extensions of various logical systems / Zoran Ognjanović, editor.

The contributions in this book survey results on combinations of probabilistic and various other classical, temporal and justification logical systems. Formal languages of these logics are extended with probabilistic operators. The aim is to provide a systematic overview and an accessible presentati...

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Bibliographic Details
Other Authors: Ognjanović, Zoran
Format: eBook
Language:English
Published: Cham : Springer, 2020.
Subjects:
Logic, Symbolic and mathematical.
Probabilities.
probability.
Computer logic
Logic, Symbolic and mathematical
Probabilities
Electronic books.
Online Access:Click for online access
Table of Contents:
  • Intro
  • Preface
  • Contents
  • List of Contributors
  • General notations and conventions
  • Chapter 1 Logics with Probability Operators
  • 1.1 Introduction
  • 1.2 The first order probability logic LFOP1 and some related logics
  • 1.2.1 Syntax
  • 1.2.2 Semantics
  • 1.2.3 Axiom system AxLFOP1
  • 1.2.4 Soundness and completeness
  • 1.2.5 Versions of the logic LFOP1
  • 1.3 Related Work
  • References
  • Chapter 2 Formalization of Probabilities with Non-linearly Ordered Ranges
  • 2.1 Introduction
  • 2.2 Logics for reasoning about p-adic valued probabilities
  • 2.2.1 p-adic numbers
  • 2.2.2 The logic LDQ
  • 2.2.3 Modeling the double-slit experiment
  • 2.2.4 Conditional p-adic probability logics
  • 2.3 Complex valued probability logics
  • 2.3.1 The logic LCOMPB
  • 2.4 Measure logic
  • 2.4.1 The logic LPG
  • 2.4.2 Extensions of the logic LPG
  • References
  • Chapter 3 Probabilistic branching time logic
  • 3.1 Introduction
  • 3.2 Temporal logics
  • 3.2.1 Linear temporal logic
  • 3.2.2 Branching time logic
  • 3.3 Probabilistic branching time logic pBTL
  • 3.3.1 Syntax and semantics
  • 3.3.2 Axiomatization
  • 3.3.3 Completeness
  • 3.4 Probabilistic reasoning about temporal information
  • 3.4.1 Syntax and semantics
  • 3.4.2 The axiomatization of PLLTL
  • 3.4.3 Completeness of Ax(PLLTL)
  • 3.4.4 Decidability
  • 3.5 Temporal reasoning about evidence
  • 3.5.1 Weight of evidence
  • 3.5.2 Reasoning about prior and posterior probabilities
  • 3.5.3 Adding temporal operators
  • 3.6 Related work
  • References
  • Chapter 4 Probabilistic Modeling of Default Reasoning
  • 4.1 Introduction
  • 4.2 Some formal systems for default reasoning
  • 4.2.1 Default logic
  • 4.2.2 Autoepistemic logic
  • 4.2.3 Circumscription
  • 4.3 Nonmonotonic consequence relations
  • 4.3.1 System P
  • 4.3.2 Conditional logic
  • 4.3.3 Logics with generalized quantifiers
  • 4.4 Probabilistic first-order logic LP, I ww
  • 4.4.1 Syntax and semantics
  • 4.4.2 Axiomatization
  • 4.4.3 Soundness and completeness
  • 4.4.4 Decidable fragments of LP, I ww
  • 4.5 Some extensions of the logic LP, I ww
  • 4.6 Applications
  • 4.7 Conclusions
  • References
  • Chapter 5 Some New Probability Operators
  • 5.1 Introduction
  • 5.1.1 Qualitative probability
  • 5.1.2 Conditional probabilities
  • 5.1.3 Independence and confirmation
  • 5.1.4 Probabilistic operators QF
  • 5.1.5 Organization of the chapter
  • 5.2 Formal languages
  • 5.3 Completeness and decidability
  • 5.4 Logics with iterations and nesting of probability operators
  • 5.5 Hierarchies of probability logics
  • 5.5.1 Upper hierarchy
  • 5.5.2 Lower hierarchy
  • 5.6 Discussion and concluding remarks
  • References
  • Chapter 6 Applications of Logics About Simple Probabilities
  • 6.1 Introduction
  • 6.1.1 Related work
  • 6.1.2 Organization of the chapter
  • 6.2 Charges generated by t-norms
  • 6.2.1 Preliminaries on charges
  • 6.2.2 Classification via e(s)

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