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Bi-state Logic

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7265)

Abstract

This paper proposes an answer to a question recently posed by Vladimir Lifschitz about which logical system would be appropriate for reasoning about logic programs with intensional functions (IF-programs for short), a type of causal logic program introduced by him in [2]. As an appropriate system we propose bi-state logic, a four-valued logic that has apparently not been previously studied. We characterize bi-state models and their logic and show how a concept of superstable (bi-state) model corresponds in the propositional case to the semantics of IF-programs. We also relate bi-state logic to classical logic and suggest its possible application in the area of program updates.

Keywords

  • Logic Program
  • Equilibrium Model
  • Classical Logic
  • Stable Model
  • Intensional Function

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Lifschitz, V.: On the logic of causal explanation (research note). Artif. Intell. 96(2), 451–465 (1997)

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  2. Lifschitz, V.: Logic programs with intensional functions (preliminary report). In: Workshop on Answer Set Programming and Other Computing Paradigms (2011)

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  3. Lifschitz, V., Pearce, D., Valverde, A.: Strongly equivalent logic programs. ACM Tr. on Computational Logic 2(4), 526–541 (2001)

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  4. Pearce, D.: A New Logical Characterization of Stable Models and Answer Sets. In: Dix, J., Przymusinski, T.C., Moniz Pereira, L. (eds.) NMELP 1996. LNCS, vol. 1216, pp. 57–70. Springer, Heidelberg (1997)

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  5. Slota, M., Leite, J.: Robust equivalence models for semantic updates of answer-set programs. In: KR 2012 (to appear, 2012)

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© 2012 Springer-Verlag Berlin Heidelberg

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Fariñas del Cerro, L., Pearce, D., Valverde, A. (2012). Bi-state Logic. In: Erdem, E., Lee, J., Lierler, Y., Pearce, D. (eds) Correct Reasoning. Lecture Notes in Computer Science, vol 7265. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30743-0_18

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  • DOI: https://doi.org/10.1007/978-3-642-30743-0_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30742-3

  • Online ISBN: 978-3-642-30743-0

  • eBook Packages: Computer ScienceComputer Science (R0)