Displaying similar documents to “Sequent Calculus, Derivability, Provability. Gödel's Completeness Theorem”

Transition of Consistency and Satisfiability under Language Extensions

Julian J. Schlöder, Peter Koepke (2012)

Formalized Mathematics

Similarity:

This article is the first in a series of two Mizar articles constituting a formal proof of the Gödel Completeness theorem [17] for uncountably large languages. We follow the proof given in [18]. The present article contains the techniques required to expand formal languages. We prove that consistent or satisfiable theories retain these properties under changes to the language they are formulated in.

Strong normalization proofs for cut elimination in Gentzen's sequent calculi

Elias Bittar (1999)

Banach Center Publications

Similarity:

We define an equivalent variant L K s p of the Gentzen sequent calculus L K . In L K s p weakenings or contractions can be performed in parallel. This modification allows us to interpret a symmetrical system of mix elimination rules L K s p by a finite rewriting system; the termination of this rewriting system can be machine checked. We give also a self-contained strong normalization proof by structural induction. We give another strong normalization proof by a strictly monotone subrecursive interpretation;...

Strong completeness of the Lambek Calculus with respect to Relational Semantics

Szabolcs Mikulás (1993)

Banach Center Publications

Similarity:

In [vB88], Johan van Benthem introduces Relational Semantics (RelSem for short), and states Soundness Theorem for Lambek Calculus (LC) w.r.t. RelSem. After doing this, he writes: "it would be very interesting to have the converse too", i.e., to have Completeness Theorem. The same question is in [vB91, p. 235]. In the following, we state Strong Completeness Theorems for different versions of LC.

First Order Languages: Further Syntax and Semantics

Marco Caminati (2011)

Formalized Mathematics

Similarity:

Third of a series of articles laying down the bases for classical first order model theory. Interpretation of a language in a universe set. Evaluation of a term in a universe. Truth evaluation of an atomic formula. Reassigning the value of a symbol in a given interpretation. Syntax and semantics of a non atomic formula are then defined concurrently (this point is explained in [16], 4.2.1). As a consequence, the evaluation of any w.f.f. string and the relation of logical implication are...

Semantics of MML Query

Grzegorz Bancerek (2012)

Formalized Mathematics

Similarity:

In the paper the semantics of MML Query queries is given. The formalization is done according to [4]

Beta-reduction as unification

A. Kfoury (1999)

Banach Center Publications

Similarity:

We define a new unification problem, which we call β-unification and which can be used to characterize the β-strong normalization of terms in the λ-calculus. We prove the undecidability of β-unification, its connection with the system of intersection types, and several of its basic properties.