Any ist-aon quantified context logic has a first-order semantics

From Semantic Portal Wiki

Edit

[[abstract::Formalized context systems of the $ist(c,\phi)$ type of Guha/McCarthy [] can be classified according to what distributivities of $ist$ over the logical connectives and quantifiers hold. We place subscripts on $ist$ to indicate the various distributivities; subscript $A$ stands for distributivity of $ist$ over conjunction and universal quantification, that is, $ist(c,\phi \wedge \psi) \leftrightarrow ist(c,\phi) \wedge ist(c,\psi)$ and $ist(c, \forall x \phi) \leftrightarrow \forall x ist(c,phi)$. Likewise $O$ stands for disjunction and existential quantification, and $N$ stands for negation. This work defines a formal language for and $ist$-type quantified context logic, and presents a model-theoretic semantics for it. It then uses this semantic machinery to formally demonstrate that when restricted to the $ist_{AON}$ case, a context logic can be given a first-order semantics.|]]

Reference:

1. Selene Makarios, Ramanathan V. Guha. Any ist-AON Quantified Context Logic has a First-Order Semantics , Knowledge Systems, AI Laboratory (KSL-06-10), 2006

bibtex

@techreport { KSL-06-10 ,
  author = "Selene Makarios, Ramanathan V. Guha", 
institution = "Knowledge Systems, AI Laboratory", 
number = "KSL-06-10", 
title = "Any ist-AON Quantified Context Logic has a First-Order Semantics", 
year = "2006", 
} 

abstract: Formalized context systems of the $ist(c,\phi)$ type of Guha/McCarthy [] can be classified according to what distributivities of $ist$ over the logical connectives and quantifiers hold. We place subscripts on $ist$ to indicate the various distributivities; subscript $A$ stands for distributivity of $ist$ over conjunction and universal quantification, that is, $ist(c,\phi \wedge \psi) \leftrightarrow ist(c,\phi) \wedge ist(c,\psi)$ and $ist(c, \forall x \phi) \leftrightarrow \forall x ist(c,phi)$. Likewise $O$ stands for disjunction and existential quantification, and $N$ stands for negation. This work defines a formal language for and $ist$-type quantified context logic, and presents a model-theoretic semantics for it. It then uses this semantic machinery to formally demonstrate that when restricted to the $ist_{AON}$ case, a context logic can be given a first-order semantics.

download:

• paper:
• slides: