Results 271 to 280 of about 32,356 (302)

FIBRED ALGEBRAIC SEMANTICS FOR A VARIETY OF NON-CLASSICAL FIRST-ORDER LOGICS AND TOPOLOGICAL LOGICAL TRANSLATION

The Journal of Symbolic Logic, 2021
AbstractLawvere hyperdoctrines give categorical algebraic semantics for intuitionistic predicate logic. Here we extend the hyperdoctrinal semantics to a broad variety of substructural predicate logics over the Typed Full Lambek Calculus, verifying their completeness with respect to the extended hyperdoctrinal semantics.
openaire   +1 more source

The complexity of resource-bounded first-order classical logic

1994
We give a finer analysis of the difficulty of proof search in classical first-order logic, other than just saying that it is undecidable. To do this, we identify several measures of difficulty of theorems, which we use as resource bounds to prune infinite proof search trees.
openaire   +2 more sources

An Extended First-Order Belnap-Dunn Logic with Classical Negation

2017
In this paper, we investigate an extended first-order Belnap-Dunn logic with classical negation. We introduce a Gentzen-type sequent calculus FBD+ for this logic and prove theorems for syntactically and semantically embedding FBD+ into a Gentzen-type sequent calculus for first-order classical logic. Moreover, we show the cut-elimination theorem for FBD+
Norihiro Kamide, Hitoshi Omori
openaire   +1 more source

Semantics of Non-Classical First Order Predicate Logics

1990
To describe semantics of a logical system one should define notions of a model and the truth in a model. A major part of classical first order model theory can be developed within the standard semantics, while alternative types of semantics (such as sheaves, forcing, polyadic algebras) play an auxiliary role.
Valentin Shehtman, Dmitrij Skvortsov
openaire   +1 more source

A modal extension of first order classical logic. II

2004
Summary: We define the semantics of the modal predicate logic introduced in Part I [ibid. 32, 165--177 (2003; Zbl 1046.03009)] and prove its soundness and strong completeness with respect to appropriate structures. These semantical tools allow us to give a simple proof that the main conservation requirement articulated in Part I is met.
Tourlakis, George, Kibedi, Francisco
openaire   +2 more sources

A Semantic Tableau Version of First-Order Quasi-Classical Logic

2001
Quasi-classical logic (QC logic) allows the derivation of non-trivial classical inferences from inconsistent information. A paraconsistent, or non-trivializable, logic is, by necessity, a compromise, or weakening, of classical logic. The compromises on QC logic seem to be more appropriate than other paraconsistent logics for applications in computing ...
openaire   +1 more source

Presheaf semantics and independence results for some non-classical first-order logics

Archive for Mathematical Logic, 1989
It is well-known that Kripke semantics for intuitionistic logic can be generalized by introducing interpretations of the logical language into toposes of set-valued functors defined on categories instead of preorders. Formally, a model is a triple \((C,X,{\mathcal I})\), where C is a small category, \(X: C\to Set\) is a functor and \({\mathcal I}\) is ...
openaire   +1 more source

First-Order Interpolation of Non-classical Logics Derived from Propositional Interpolation

2017
This paper develops a general methodology to connect propositional and first-order interpolation. In fact, the existence of suitable skolemizations and of Herbrand expansions together with a propositional interpolant suffice to construct a first-order interpolant.
Matthias Baaz, Anela Lolic
openaire   +1 more source

α lean TA P: A Declarative Theorem Prover for First-Order Classical Logic

2008
We present α lean TA P , adeclarative tableau-based theorem prover written as a purerelation. Like lean TA P , on which it is based,α lean TA P can prove groundtheorems in first-order classical logic. Since it is declarative,α lean TA P generates theorems and accepts non-ground theorems and proofs.
Joseph P. Near, William E. Byrd, Daniel P. Friedman   +2 more
openaire   +1 more source

How game-theoretical semantics works: Classical first-order logic

Erkenntnis, 1988
The structure of strategies for semantical games is studied by means of a new formalism developed for the purpose. Rigorous definitions of strategy, winning strategy, truth, and falsity are presented. Non-contradiction and bivalence are demonstrated for the truth-definition.
openaire   +1 more source