Any $ist_{AON}$ Quantified Context Logic has a First-Order Semantics.

Reference: Makarios, S.; Guha, R.V. Any $ist_{AON}$ Quantified Context Logic has a First-Order Semantics. 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.


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