A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Extended normal form theorems for logical proofs from axioms

2000
*
Theoretical Computer Science
*

We present an exact modeling of cut-free arithmetic by cut-free predicate

doi:10.1016/s0304-3975(99)00172-3
fatcat:zb4a6lksx5f47h6koahsbkwsiu
*logic*. Exact prooftheoretic analysis reveals connections with omega-consistency and re ection. ... First, we present here a short*proof*of these results which*extends*the*proof*in [4] . Second, we prove this*normal**form**theorem*by a transÿnite induction. ... we prove the*extended**normal**form**theorem*,*Theorem*2 by a transÿnite induction up to the nth epsilon number n . ...##
###
General Recursive Functions in the Number-Theoretic Formal System

1957
*
Annals of the Japan Association for Philosophy of Science
*

*For*any LK or LJ-provable sequent, there exists an LK-or LJ-

*proof*of the sequent which contains no cut, respectively. 1. 52.

*EXTENDED*

*NORMAL*

*FORM*

*THEOREM*ON LK. ... By ƒ¡a we denote the following

*axiom*system: By Gentzen's Consistency

*theorem*and

*Extended*

*normal*

*form*

*theorem*on LK, it can be immediately proved that Pa is consistent . ...

##
###
Proof systems for structured algebraic specifications: An overview
[chapter]

1997
*
Lecture Notes in Computer Science
*

*proof*systems

*for*the underlying

*logic*, may be used

*for*deriving

*theorems*of the specification. ... In the

*normal*

*form*approach of Bergstra, Hering and Klint, a flat set of

*axioms*is constructed

*for*each structured specification, whereas in the second approach not only individual

*axioms*but also individual ... can be derived

*from*the

*axioms*of its

*normal*

*form*nf(SP) (using some standard

*proof*system of the underlying

*logic*). ...

##
###
The foundation of a generic theorem prover

1989
*
Journal of automated reasoning
*

Examples illustrate the use of this meta-

doi:10.1007/bf00248324
fatcat:5fmyfn4pozfipbogumbiqm5iji
*logic*to formalize*logics*and*proofs*.*Axioms**for*first-order*logic*are shown to be sound and complete. ... Section 6*extends*the backwards*proof*methods to handle quantifiers and unification, with examples*from*first-order*logic*. The representation of eigenvariables differs*from*Isabelle-86. ... The*normal**form*does not take account of the*logical*rules. No effective procedure can reduce every*theorem*to some unique true formula. There is also a*normalization*procedure*for*HOL*proofs*. ...##
###
Page 217 of Mathematical Reviews Vol. 33, Issue 2
[page]

1967
*
Mathematical Reviews
*

*for*arith- metic

*from*a

*normal*-

*form*

*theorem*. ... With the second version of deduction, a

*normal*-

*form*

*theorem*results, none with the first. The system of relevant implication is

*extended*to the minimal and classical

*logics*. ...

##
###
Adding the everywhere operator to propositional logic

1998
*
Journal of Logic and Computation
*

First, introducing an inference rule textual substitution allows seamless integration of the propositional and modal parts of the

doi:10.1093/logcom/8.1.119
fatcat:cmxdfxyb5jb6tpwyw55eb5mktu
*logic*, giving a more practical system*for*writing formal*proofs*. ... Second, the two following approaches to axiomatizing a*logic*are shown to be not equivalent: (i) give*axiom*schemes that denote an infinite number of*axioms*and (ii) write a finite number of*axioms*in ... Leino, and members of the Eindhoven Tuesday Afternoon Club*for*their extremely helpful comments on drafts of this paper. ...##
###
Realization Theorems for Justification Logics: Full Modularity
[chapter]

2015
*
Lecture Notes in Computer Science
*

A uniform realization

doi:10.1007/978-3-319-24312-2_16
fatcat:s6dznxculjgevpuz6njzvw3cuu
*theorem**for*all the modal*logics*of the socalled modal cube, i.e.,*for*the extensions of the basic modal*logic*K with any subset of the*axioms*d, t, b, 4, and 5, has been proven using ... A constructive*proof*of a realization*theorem*typically relies on a cut-free sequent-style*proof*system*for*the corresponding modal*logic*. ... The authors are indebted to Agata Ciabattoni*for*making this research possible. ...##
###
Extracting Herbrand Disjunctions by Functional Interpretation

2003
*
BRICS Report Series
*

Carrying out a suggestion by Kreisel, we adapt Gödel's functional interpretation to ordinary first-order predicate

doi:10.7146/brics.v10i32.21800
fatcat:5or2zw5funfgrjillgor6ravz4
*logic*(PL) and thus devise an algorithm to extract Herbrand terms*from*PL-*proofs*. ... The algorithm consists of two main steps: first we extract a functional realizer, next we compute the beta-*normal*-*form*of the realizer*from*which the Herbrand terms can be read off. ... The*theorem*also*extends*to tuples ∃x of quantifiers.*Proof*. The*theorem*follows*from*the above propositions and lemmas. ...##
###
Algebraic semantics for a modal logic close to S1

2014
*
Journal of Logic and Computation
*

Suszko's non-Fregean

doi:10.1093/logcom/exu067
fatcat:evsrcc2lvjb4hopeeawn7nzvuq
*logic*adapted to the language of modal*logic*(we call these*axioms*the*axioms*of propositional identity). ... Lewis as*logics**for*strict implication. While there are Kripke semantics*for*S2 and S3, there is no known natural semantics*for*S1. ...*Proof*. Symmetry of ≈ Φ follows*from*propositional*logic*. Since ϕ → ϕ is an*axiom*, we get (ϕ → ϕ) ∈ Φ by rule AN. Thus, ≈ Φ is reflexive. Transitivity follows*from*the scheme of*axioms*(iii). ...##
###
On Natural Deduction for Herbrand Constructive Logics III: The Strange Case of the Intuitionistic Logic of Constant Domains
[article]

2018
*
arXiv
*
pre-print

The

arXiv:1803.07313v1
fatcat:6d34nxyihvdl5fnbon7ndn3kaq
*logic*of constant domains is intuitionistic*logic**extended*with the so-called forall-shift*axiom*, a classically valid statement which implies the excluded middle over decidable formulas. ... Surprisingly, this*logic*is constructive and so far this has been proved by cut-elimination*for*ad-hoc sequent calculi. ...*theorem**for*CD easily follows*from*Proposition 6. ...##
###
Proof normalization for a first-order formulation of higher-order logic
[chapter]

1997
*
Lecture Notes in Computer Science
*

We show that the

doi:10.1007/bfb0028389
fatcat:3atzp7es2fbj7n5uj67ksw4fdy
*proof*of the*normalization**theorem**for*the usual formulation of higher-order*logic*can be adapted to prove*normalization**for*its rst-order formulation. ... Thus,*from*the point of view of*proof**normalization*, de ning higher-order*logic*as a di erent*logic*or as a rst-order theory does not matter. ... The so called*proof**normalization**theorem**for*rst-order*logic*is only a*proof**normalization**theorem**for*the empty theory in rst-order*logic*. ...##
###
An Axiomatization for Cylinder Computation Model
[chapter]

2014
*
Lecture Notes in Computer Science
*

To model and verify multi-core parallel programs, the paper proposes an

doi:10.1007/978-3-319-08783-2_7
fatcat:ny5srglrtrfofatrvyv2acresu
*axiom*system*for*Propositional Projection Temporal*Logic*with Cylinder Computation Model (CCM-PPTL). ... Moreover, the*axiom*system of CCM-PPTL is established by*extending*that of PPTL with some*axioms*and inference rules of CCM operators. ... Further, to provide a highly automatical verification approach, the existing tool*for*PPTL*theorem*proving will be*extended*to support CCM operators. ...##
###
Expanding the Realm of Systematic Proof Theory
[chapter]

2009
*
Lecture Notes in Computer Science
*

This paper is part of a general project of developing a systematic and algebraic

doi:10.1007/978-3-642-04027-6_14
fatcat:xofdlspf6jentdd63tha3b7idq
*proof*theory*for*nonclassical*logics*. ... Our method also works as a heuristic principle*for*finding appropriate rules*for**axioms*located at levels higher than P 3 . ...*Proof*We have φ •− −• j k ( l ξ j,k,l ) 1 where ξ j,k,l is N 2 -*normal*,*From*N 2 -*axioms*to Sequent Rules In this section we provide an algorithm*for*transforming N 2*axioms*into equivalent sequent calculus ...##
###
An Arithmetical Interpretation of Verification and Intuitionistic Knowledge
[chapter]

2015
*
Lecture Notes in Computer Science
*

The BHK interpretation of intuitionistic

doi:10.1007/978-3-319-27683-0_22
fatcat:qmeraepqdzdqbcfmdlnjwncgq4
*logic*has a precise formulation in the*Logic*of*Proofs*and its arithmetical semantics. ... We show here that this interpretation can be*extended*to the notion of verification upon which intuitionistic knowledge is based, thereby providing the systems of intuitionistic epistemic*logic**extended*... The question about exact interpretations*for*other intuitive readings of these*logics*is left*for*further investigation. ...##
###
Classical Modal Display Logic in the Calculus of Structures and Minimal Cut-free Deep Inference Calculi for S5

2007
*
Journal of Logic and Computation
*

Since every CMDL calculus enjoys cut-elimination, we obtain a cut-elimination

doi:10.1093/logcom/exm026
fatcat:wu7krho5tnh3rnjuorwgnfi5fm
*theorem**for*all corresponding CoS calculi. ... We then show how our result leads to a minimal cut-free CoS calculus*for*modal*logic*S5. No other existing CoS calculi*for*S5 enjoy both these properties simultaneously. ... Acknowledgement We thank Kai Bru¨nnler and the anonymous referees*for*their comments on an earlier version of the article. ...
« Previous

*Showing results 1 — 15 out of 25,948 results*