Results 241 to 250 of about 506,932 (281)

On the Undecidability of Some Sub-classical First-Order Logics

1999
A general criterion for the undecidabily of sub-classical first-order logics and important fragments thereof is established. It is applied, among others, to Urquart's (original version of) C and the closely related logic C*. In addition, hypersequent systems for (first-order) C and C* are introduced and shown to enjoy cut-elimination.
Matthias Baaz, Agata Ciabattoni, Christian Fermüller, Helmut Veith   +3 more
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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.
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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
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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 ...
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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
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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
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First Order Extensions of Classical Systems of Modal Logic; The role of the Barcan schemas

Studia Logica, 2002
The paper studies first order extensions of classical systems of modal logic (see (Chellas, 1980, part III)). We focus on the role of the Barcan formulas. It is shown that these formulas correspond to fundamental properties of neighborhood frames.
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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
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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 ...
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Structured Sequent Calculi for Combining Intuitionistic and Classical First-Order Logic

2000
We define a sound and complete logic, called \({\cal FO}^{\supset}\), which extends classical first-order predicate logic with intuitionistic implication.
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