Propositional dynamic logic with Belnapian truth values
نویسنده
چکیده
We introduce BPDL, a combination of propositional dynamic logic PDL with the basic four-valued modal logic BK studied by Odintsov and Wansing (‘Modal logics with Belnapian truth values’, J. Appl. Non-Class. Log. 20, 279–301 (2010)). We modify the standard arguments based on canonical models and filtration to suit the four-valued context and prove weak completeness and decidability of BPDL.
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 کاملA Dynamic Logic Framework for Abstract Argumentation
We provide a logical analysis of abstract argumentation frameworks and their dynamics. Following previous work by several authors, we express attack relation and argument status by means of propositional variables and define acceptability criteria by formulas of propositional logic. We here study the dynamics of argumentation frameworks in terms of basic operations on these propositional variab...
متن کاملTableaux for Dynamic Logic of Propositional Assignments
The Dynamic Logic for Propositional Assignments (DL-PA) has recently been studied as an alternative to Propositional Dynamic Logic (PDL). In DL-PA, the abstract atomic programs of PDL are replaced by assignments of propositional variables to truth values. This makes DL-PA enjoy some interesting meta-logical properties that PDL does not, such as eliminability of the Kleene star, compactness and ...
متن کاملA Mathematical Setting for Fuzzy Logics
The setup of a mathematical propositional logic is given in algebraic terms, describing exactly when two choices of truth value algebras give the same logic. The propositional logic obtained when the algebra of truth values is the real numbers in the unit interval equipped with minimum, maximum and :x = 1 x for conjunction, disjunction and negation, respectively, is the standard propositional f...
متن کاملGödel-Dummett Predicate Logics and Axioms of Prenexability
Gödel-Dummett logic in general is a multi-valued logic where a truth value of a formula can be any number from the real interval [0, 1] and where implication → is evaluated via the Gödel implication function. As to truth values, 0 (falsity) and 1 (truth) are the extremal truth values whereas the remaining truth values are called intermediate. Gödel implication function ⇒ is defined as follows: ...
متن کامل