From Newsgroup: comp.theory

William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion

A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication

The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.

https://philarchive.org/archive/SZMASL
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Copyright 2026 Olcott

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
The complete structure of this system is now defined.

The entire body of knowledge expressed in language is
comprised of two types of relations between finite strings:
(a) *Axioms* Expressions of language that are stipulated to be true.

My system bridges the analytic/synthetic distinction by
expressly encoding all empirical "atomic facts" in a formal
language such as CycL of the Cyc project.

(b) *Inference Rules* Expressions of language that are semantically
entailed syntactically from (a) and/or (b).

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