Giovanna Corsi

Completeness theorem for dummett's LC quantified and some of its extensions

AbstractDummetts logic LC quantified, Q-LC, is shown to be characterized by the extended frame 〈Q+, ≤,D〉, where Q+ is the set of non-negative rational numbers, ≤is the numerical relation “less or equal then” and D is the domain function such that for all v, w ∈ Q+, Dv ≠ φ and if v ≤ w, then Dv. Dvn

Problems in set theory, mathematical logic, and the theory of algorithms

subseteq

Bull's Theorem by the Method of Diagrams

nDw. Moreover, simple completeness proofs of extensions of Q-LC are given.

Weak Logics with Strict Implication

The aim of this paper is to provide a decision procedure for Dummetts logic LC, such that with any given formula will be associated either a proof in a sequent calculus equivalent to LC or a finite linear Kripke countermodel.

A Cut-Free Calculus For Dummett's LC Quantified

Preface. I: Problems. 1. Set theory. 1.1. Operations on sets. 1.2. Relations and functions. 1.3. Special binary relations. 1.4. Cardinal numbers. 1.5. Ordinal numbers. 1.6. Operations on cardinal numbers. 2: Algebra. 2.1. Algebra of propositions. 2.2. Truth functions. 2.3. Propositional calculi. 2.4. The language of predicate logic. 2.5. Satisfiability of predicate formulas. 2.6. Predicate calculi. 2.7. Axiomatic theories. 2.8. Reduced products. 2.9. Axiomatizable classes. 3: Theory of algorithms. 3.1. Partial recursive functions. 3.2. Turing machines. 3.3. Recursive and recursively enumerable sets. 3.4. Kleene and Post numberings. II: Solutions. 1. Set theory. 1.1. Operations on sets. 1.2. Relations and functions. 1.3. Special binary relations. 1.4. Cardinal numbers. 1.5. Ordinal numbers. 1.6. Operations on cardinal numbers. 2. Mathematical logic. 2.1. Algebra of propositions. 2.2. Truth functions. 2.3. Propositional calculi. 2.4. The language of predicate logic. 2.5. Satisfiability of predicate formulas. 2.6. Predicate calculi. 2.7. Axiomatic theories. 2.8. Reduced products. 2.9. Axiomatizable classes. 3: Theory of algorithms. 3.1. Partial recursive functions. 3.2. Turing machines. 3.3. Recursive and recursively enumerable sets. 3.4. Kleene and Post numberings. References. Index.

A unified completeness theorem for quantified modal logics

In this chapter we study n-ary partial functions f n (x1,…,x n ) (n = 1, 2,…) over natural numbers, i.e., functions whose domains are subsets of N n and whose values are natural numbers. We say that f n (x1,…,x n ) is defined if 〈x1,…,x n 〉 ∈ δ fn and undefined otherwise. For any a1,…,a n ∈ N and any partial functions f k and g s we write (a i 1,…,a ik ) = g(a j 1,…,a js ) if the corresponding values are both undefined or if they both exist and coincide. An n-ary function f n (x1,…,x n ) is called total if δ fn = N n .

Bridging the gap: philosophy, mathematics, and physics

We show how to use diagrams in order to obtain straightforward completeness theorems for extensions of K4.3 and a very simple and constructive proof of Bulls theorem: every normal extension of S4.3 has the finite model property.