The Inverse Method for Many-Valued Logics
نویسندگان
چکیده
We define an automatic proof procedure for finitely manyvalued logics given by truth tables. The proof procedure is based on the inverse method. To define this procedure, we introduce so-called introduction-based sequent calculi. By studying proof-theoretic properties of these calculi we derive efficient validityand satisfiability-checking procedures based on the inverse method. We also show how to translate the validity problem for a formula to unsatisfiability checking of a set of propositional clauses.
منابع مشابه
Truth Values and Connectives in Some Non-Classical Logics
The question as to whether the propositional logic of Heyting, which was a formalization of Brouwer's intuitionistic logic, is finitely many valued or not, was open for a while (the question was asked by Hahn). Kurt Gödel (1932) introduced an infinite decreasing chain of intermediate logics, which are known nowadays as Gödel logics, for showing that the intuitionistic logic is not finitely (man...
متن کاملDyadic semantics for many-valued logics
This paper obtains an effective method which assigns two-valued semantics to every finite-valued truth-functional logic (in the direction of the so-called “Suszko’s Thesis”), provided that its truth-values can be individualized by means of its linguistic resources. Such two-valued semantics permit us to obtain new tableau proof systems for a wide class of finitevalued logics, including the main...
متن کاملSuszko’s Thesis and dyadic semantics
A well-known result by Wójcicki-Lindenbaum shows that any tarskian logic is many-valued, and another result by Suszko shows how to provide 2-valued semantics to these very same logics. This paper investigates the question of obtaining 2-valued semantics for many-valued logics, including paraconsistent logics, in the lines of the so-called “Suszko’s Thesis”. We set up the bases for developing a ...
متن کاملAutomatic extraction of axiomatizations in terms of two-signed tableaux for finite-valued logics
Classical Logic is bivalent in that it admits exactly two truth-values: the true and the false. Many-valued logics, in contrast, allow for the consideration of arbitrarily large classes of truth-values. To export the canonical notion of entailment to the realm of many-valuedness, the trick is to characterize any such class of truth-values by saying that some of these values are ‘designated’. On...
متن کاملReduction of Many-valued into Two-valued Modal Logics
In this paper we develop a 2-valued reduction of many-valued logics, into 2-valued multi-modal logics. Such an approach is based on the contextualization of many-valued logics with the introduction of higher-order Herbrand interpretation types, where we explicitly introduce the coexistence of a set of algebraic truth values of original many-valued logic, transformed as parameters (or possible w...
متن کامل