Contradiction-Tolerant Process Algebra with Propositional Signals

Abstract

In a previous paper, an ACP-style process algebra was proposed in which propositions are used as the visible part of the state of processes and as state conditions under which processes may proceed. This process algebra, called ACPps, is built on classical propositional logic. In this paper, we present a version of ACPps built on a paraconsistent propositional logic which is essentially the same as CLuNs. There are many systems that would have to deal with self-contradictory states if no special measures were taken. For a number of these systems, it is conceivable that accepting self-contradictory states and dealing with them in a way based on a paraconsistent logic is an alternative to taking special measures. The presented version of ACPps can be suited for the description and analysis of systems that deal with self-contradictory states in a way based on the above-mentioned paraconsistent logic.

On the strongest three-valued paraconsistent logic contained in classical logic and its dual

“…There is text overlap between this note and [7]. This note generalizes and elaborates Section 2 of that paper in such a way that it may be of independent importance to the area of paraconsistent logics.…”

“…Actually, property (c) can be strengthened to the following property: for all formulas A of LP ⊃,F , ⊢ A iff ⊢ CL A. In [7], properties (e) and (f) are considered desirable and essential, respectively, for a paraconsistent propositional logic on which a process algebra that allows for dealing with contradictory states is built.…”

“…Because 'nondeterministic truth tables' that uniquely characterize the 8192 three-valued paraconsistent propositional logics with properties (a) and (b) are given in [2], 2 the theorem can be proved by showing that, for each of the connectives, only one of the ordinary truth tables represented by the non-deterministic truth table for that connective is compatible with the laws given in Table 2. It can be shown by short routine case analyses that only one of the 8 ordinary truth tables represented by the non-deterministic truth tables for conjunction is compatible with laws (1), (3), (5), and (7), only one of the 32 ordinary truth tables represented by the non-deterministic truth tables for disjunction is compatible with laws (2), ( 4), (6), and ( 8), and only one of the 2 ordinary truth tables represented by the non-deterministic truth table for negation is compatible with law (9). Given the ordinary truth table for conjunction, disjunction, and negation so obtained, it can be shown by short routine case analyses that only one of the 16 ordinary truth tables represented by the non-deterministic truth table for implication is compatible with laws ( 10) and (11).…”

A classical-logic view of a paraconsistent logic

“…In [2], an application of LP ⊃,F can be found. The properties of the logical equivalence relation that are essential for that application, among which most, but not all, properties considered desirable above, reduces the number of ideal three-valued paraconsistent propositional logics that are applicable even to 1, namely LP ⊃,F .…”

Sumterms, Summands, Sumtuples, and Sums and the Meta-arithmetic of Summation

“…In [6] an application of paraconsistency in the setting of arithmetical datatypes is developed. An application of condition tolerance via paraconsistency is developed in detail in [8]. For a survey on paraconsistent logics I mention [17] and [18].…”