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TRANSITIVE PRIMAL INFON LOGIC

Published online by Cambridge University Press:  21 March 2013

CARLOS COTRINI  and
YURI GUREVICH
CARLOS COTRINI*
Affiliation:
Swiss Federal Institute of Technology
YURI GUREVICH*
Affiliation:
Microsoft Research
*
*CARLOS COTRINI, SWISS FEDERAL INSTITUTE OF TECHNOLOGY, ZÜ RICH, SWITZERLAND E-mail: ccarlos@student.ethz.ch
†YURI GUREVICH, MICROSOFT RESEARCH, REDMOND, WA 98052 E-mail: gurevich@microsoft.com
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Abstract

Primal infon logic was introduced in 2009 in connection with access control. In addition to traditional logic constructs, it contains unary connectives p said indispensable in the intended access control applications. Propositional primal infon logic is decidable in linear time, yet suffices for many common access control scenarios. The most obvious limitation on its expressivity is the failure of the transitivity law for implication: $x \to y$ and $y \to z$ do not necessarily yield $x \to z$. Here we introduce and investigate equiexpressive “transitive” extensions TPIL and TPIL* of propositional primal infon logic as well as their quote-free fragments TPIL0 and TPIL0* respectively. We prove the subformula property for TPIL0* and a similar property for TPIL*; we define Kripke models for the four logics and prove the corresponding soundness-and-completeness theorems; we show that, in all these logics, satisfiable formulas have small models; but our main result is a quadratic-time derivation algorithm for TPIL*.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 6 , Issue 2 , June 2013 , pp. 281 - 304
Copyright
Copyright © Association for Symbolic Logic 2013 

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