Two sets of formulas have been deduced in the process.
In the \(m\ -valued case, these are sequences of length \(m\ -valueds of formulas.
(For the moment, capital Greek letters range over sets of formulas).
A set of equations Eq in one variable defines a translation from formulas to sets of equations: each formula is translated into the set of equations Eq. Similarly, a set of formulas Δ p, q) in two variables defines a translation from equations to sets of formulas: each equation φ ≈ ψ is translated into the set of formulas Δ.
A Hilbert consequence relation is a relation between pairs of formulas, a Tarski relation is a relation between sets of formulas (possibly infinite) and individual formulas, and a Scott relation is a relation between two sets of formulas.
The postulates for merging consider a multi-set of sets of formulas (belief profile, or belief set, the terminology used in early papers) \(E = \{K_1, \ldots, K_{n}\}\).
Within modular semantics propositions receive the usual classical truth values and justifications are interpreted syntactically as sets of formulas.
In this report, two sets of formulas to calculate the mechanical spectra of deposited materials are further analyzed.
We propose a language LS for expressing assertions about strings, and study in detail two sets of formulas ΣB0, a set of formulas decidable in polytime, and ΣB1, a set of formulas with the property that those provable in S yield polytime algorithms.
Note that whereas propositions in modular models are interpreted semantically, as truth values, justifications are interpreted syntactically, as sets of formulas.
