On Knowledge, Strings, and Paradoxes

@inproceedings{Kerber1998OnKS,
  title={On Knowledge, Strings, and Paradoxes},
  author={Manfred Kerber},
  booktitle={JELIA},
  year={1998}
}
A powerful syntactic theory as well as expressive modal logics have to deal with self-referentiality. Self-referentiality and paradoxes seem to be close neighbours and depending on the logical system, they have devastating consequences, since they introduce contradictions and trivialise the logical system. There is a large amount of different attempts to tackle these problems. Some of them are compared in this paper, futhermore a simple approach based on a three-valued logic is advocated. In… 
4 Citations
Living with Paradoxes
  • Manfred Kerber
  • Computer Science, Philosophy
    Electron. Notes Theor. Comput. Sci.
  • 2005
On Truth, Knowledge, Strings, and Paradoxes
One of the key issues in artiicial intelligence is the representation and processing of knowledge. The selection of an appropriate formalism for doing so is a crucial step in building a usable
Self-Referencing Languages Revisited
TLDR
The present semantic analysis of the problem components concludes that the traditional language of logic fails to detect Tarski’s paradox, since the formalised version of the liar sentence does not represent a correct definition.
Logical Theories for Agent Introspection
TLDR
This chapter discusses self-reference and logic, from logic programming semantics to the consistency of syntactical treatments of knowledge and belief, and restricted truth predicates in first-order logic.

References

SHOWING 1-10 OF 32 REFERENCES
Languages with Self-Reference II: Knowledge, Belief, and Modality
Mechanising Partiality With Re-implementation
TLDR
It is shown, that it is possible to enhance a two-valued theorem prover by a simple strategy so that it can be used to generate proofs for the theorems of the three-valued setting.
Languages With Self-Reference I: Foundations
A Mechanization of Strong Kleene Logic for Partial Functions
TLDR
This paper presents a resolution calculus that combines the proper treatment of partial functions with the efficiency of sorted calculi, and applies recent methods from sorted logics.
A Tableau Calculus for Partial Functions
Even though it is not very often admitted, partial functions do play a significant role in many practical applications of deduction systems. Kleene has already given a semantic account of partial
Representations of commonsense knowledge
  • E. Davis
  • Education
    notThenot Morgan Kaufmann series in representation and reasoning
  • 1990
From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931
The fundamental texts of the great classical period in modern logic, some of them never before available in English translation, are here gathered together for the first time. Modern logic, heralded
Handbook of logic in artificial intelligence and logic programming (vol. 1)
TLDR
A good way to break the boredom in reading is choosing handbook of logic in artificial intelligence and logic programming vol 3 nonmonotonic reasoning a as the reading material.
Prolegomena to a Theory of Mechanized Formal Reasoning
The Liar: An Essay on Truth and Circularity
INTRODUCTION: The Liar Sentences, statements, and Propositions The universe of hypersets RUSSELLIAN PROPOSITIONS AND THE LIAR: Modeling Russellian propositions Truth of Russellian propositions
...
...