Universal Models for the Positive Fragment of Intuitionistic Logic
نویسندگان
چکیده
We study the n-universal model of the [∨,∧,→]-fragment of the intuitionistic propositional calculus IPC. We denote it by U(n) and show that it is isomorphic to a generated submodel of the n-universal model of IPC, which is denoted by U(n). We show that this close resemblance makes U(n) mirror many properties of U(n). Using U(n), we give an alternative proof of Jankov’s theorem stating that the intermediate logic KC, the logic of the weak excluded middle, is the greatest intermediate logic extending IPC that proves exactly the same negationfree formulas as IPC.
منابع مشابه
Duality and Universal Models for the Meet-Implication Fragment of IPC
In this paper we investigate the fragment of intuitionistic logic which only uses conjunction (meet) and implication, using finite duality for distributive lattices and universal models. We give a description of the finitely generated universal models of this fragment and give a complete characterization of the up-sets of Kripke models of intuitionistic logic which can be defined by meet-implic...
متن کاملPositive Formulas in Intuitionistic and Minimal Logic
In this article we investigate the positive, i.e. ¬,⊥-free formulas of intuitionistic propositional and predicate logic, IPC and IQC, and minimal logic, MPC and MQC. For each formula φ of IQC we define the positive formula φ that represents the positive content of φ. The formulas φ and φ exhibit the same behavior on top models, models with a largest world that makes all atomic sentences true. W...
متن کاملTruth 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 کاملAN ALGEBRAIC STRUCTURE FOR INTUITIONISTIC FUZZY LOGIC
In this paper we extend the notion of degrees of membership and non-membership of intuitionistic fuzzy sets to lattices and introduce a residuated lattice with appropriate operations to serve as semantics of intuitionistic fuzzy logic. It would be a step forward to find an algebraic counterpart for intuitionistic fuzzy logic. We give the main properties of the operations defined and prove som...
متن کاملThe Universal Model for the Negation-free Fragment of IPC
We identify the universal n-model of the negation-free fragment of the intuitionistic propositional calculus IPC. We denote it by U(n) and show that it is isomorphic to a generated submodel of the universal n-model of IPC, which is denoted by U(n). We show that this close resemblance makes U(n) mirror many properties of U(n). Finally, using U(n), we give an alternative proof of Jankov’s Theorem...
متن کامل