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  1. Peter Apostoli (2000). The Analytic Conception of Truth and the Foundations of Arithmetic. Journal of Symbolic Logic 65 (1):33-102.
  2. Peter Apostoli (1997). On the Completeness of First Degree Weakly Aggregative Modal Logics. Journal of Philosophical Logic 26 (2):169-180.
    This paper extends David Lewis' result that all first degree modal logics are complete to weakly aggregative modal logic by providing a filtration-theoretic version of the canonical model construction of Apostoli and Brown. The completeness and decidability of all first-degree weakly aggregative modal logics is obtained, with Lewis's result for Kripkean logics recovered in the case k = 1.
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  3. Peter Apostoli (1996). Modal Aggregation and the Theory of Paraconsistent Filters. Mathematical Logic Quarterly 42 (1):175-190.
    This paper articulates the structure of a two species of weakly aggregative necessity in a common idiom, neighbourhood semantics, using the notion of a k-filter of propositions. A k-filter on a non-empty set I is a collection of subsets of I which contains I, is closed under supersets on I, and contains ∪{Xi ≤ Xj : 0 ≤ i < j ≤ k} whenever it contains the subsets X0,…, Xk. The mathematical content of the proof that weakly aggregative modal logic (...)
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  4. Peter Apostoli & Bryson Brown (1995). A Solution to the Completeness Problem for Weakly Aggregative Modal Logic. Journal of Symbolic Logic 60 (3):832-842.