The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.

## Filters

##
###
Page 117 of The Philosophical Review Vol. 67, Issue 1
[page]

1958
*
The Philosophical Review
*

Chapter III discusses a formulation

*of**the**first**order**functional**calculus*short*of*a*completeness*proof. ... But it is certainly not as interesting as*the**completeness*result for*the**first**order**functional**calculus*. ...##
###
Teaching a Formalized Logical Calculus

2020
*
Electronic Proceedings in Theoretical Computer Science
*

We present soundness and

doi:10.4204/eptcs.313.5
fatcat:6mjb5dae3beizfqa2ncyjtmo4y
*completeness*proofs*of*a sequent*calculus*for*first*-*order*logic, formalized in*the*interactive proof assistant Isabelle/HOL. ... We strive to not only present*the*results*of**the*proofs*of*soundness and*completeness*, but also to provide a deep dive into a programming-like approach to*the*formalization*of**first*-*order*logic syntax, ... (2018): Formalization*of**the*Resolution*Calculus*for*First*-*Order*Logic. ...##
###
Page 1992 of Mathematical Reviews Vol. , Issue 94i
[page]

1994
*
Mathematical Reviews
*

Summary: “

*The*model elimination*calculus*is a linear, refutation- ally*complete**calculus*for*first*-*order*clause logic. We show how to extend this*calculus*with a framework for theory reasoning. ...*The*theory (called axiomatic*function*theory, or AFT) is described in*the*language*of*classical*first*-*order*predicate logic with equality and one nonlogical predicate symbol for*function*application. ...##
###
Lambda Logic
[chapter]

2004
*
Lecture Notes in Computer Science
*

Lambda logic is

doi:10.1007/978-3-540-25984-8_34
fatcat:vqfgfabukfhbdb6fp6ugxz45ka
*the*union*of**first**order*logic and lambda*calculus*. We prove basic metatheorems for both total and partial versions*of*lambda logic. ... We use lambda logic to state and prove a soundness theorem allowing*the*use*of*second*order*unification in resolution, demodulation, and paramodulation in a*first*-*order*context. ... Introduction*The*twentieth century saw*the*flowering*of**first**order*logic, and*the*invention and development*of**the*lambda*calculus*. ...##
###
Superposition with First-class Booleans and Inprocessing Clausification
[chapter]

2021
*
Lecture Notes in Computer Science
*

AbstractWe present a

doi:10.1007/978-3-030-79876-5_22
fatcat:ndddytox3vcefnvnk6xvglqyhi
*complete*superposition*calculus*for*first*-*order*logic with an interpreted Boolean type. ... Working directly on formulas, our*calculus*avoids*the*costly axiomatic encoding*of**the*theory*of*Booleans into*first*-*order*logic and offers various ways to interleave clausification with other derivation ... We refer to our technical report [25] for more details on our*calculus*and*the**complete**completeness*proof. Logic Our logic is a*first*-*order*logic with an interpreted Boolean type. ...##
###
Page 4293 of Mathematical Reviews Vol. , Issue 94h
[page]

1994
*
Mathematical Reviews
*

*The*many-valued

*first*-

*order*predicate calculi

*of*Post are specifically studied. ...

*of*calculi being

*functionally*

*complete*and

*the*proofs

*of*their

*completeness*and decidability being obtained. ...

##
###
A Combinator-Based Superposition Calculus for Higher-Order Logic
[chapter]

2020
*
Lecture Notes in Computer Science
*

We present a refutationally

doi:10.1007/978-3-030-51074-9_16
fatcat:tw3vp2xhnffo7m7gv5ymma4c2a
*complete*superposition*calculus*for a version*of*higher-*order*logic based on*the*combinatory*calculus*. We also introduce a novel method*of*dealing with extensionality. ...*The**calculus*was implemented in*the*Vampire theorem prover and we test its performance against other leading higher-*order*provers.*The*results suggest that*the*method is competitive. ...*The**first*author thanks*the*family*of*James Elson for funding his research. ...##
###
Page 6736 of Mathematical Reviews Vol. , Issue 98K
[page]

1998
*
Mathematical Reviews
*

We show that strong normalization is a modular property

*of*all*the*systems in*the*algebraic-A-cube, provided that*the**first*-*order*rewrite rules are nonduplicating and*the*higher-*order*rules satisfy*the*... Summary: “We present*the*algebraic-A-cube, an extension*of*Barendregt’s A-cube with*first*- and higher-*order*algebraic rewrit- ing. ...##
###
Kurt Gödel and Computability Theory
[chapter]

2006
*
Lecture Notes in Computer Science
*

In particular, Gödel's 1931 paper on incompleteness and

doi:10.1007/11780342_59
fatcat:mi2qey4monflhagqyijp3wqjfi
*the*methods developed therein were important for*the*early development*of*recursive*function*theory and*the*lambda*calculus*at*the*hands*of*Church ... Although Kurt Gödel does not figure prominently in*the*history*of*computabilty theory, he exerted a significant influence on some*of**the*founders*of**the*field, both through his published work and through ... In a related sense, this was also*the*basis for Hilbert's conjecture that*first*-*order*logic is*complete*in*the*sense that any valid sentence is derivable from*the*axioms*of**the*predicate*calculus*. ...##
###
Page 302 of The American Mathematical Monthly Vol. 59, Issue 4
[page]

1952
*
The American Mathematical Monthly
*

Additional Methods for Equa- tions

*of**the**First**Order*and*First*Degree . Orthogonal Trajectories . Hyperbolic*Functions*. Linear Equations with Con- stant Coefficients . ... Ready in April CONTENTS Elimination*of*11. Variation*of*Parameters and . Definitions, Arbitrary Constants . Equations*of**the**First**Order*and*First*Degree . ...##
###
The semantics of second-order lambda calculus

1990
*
Information and Computation
*

In

doi:10.1016/0890-5401(90)90044-i
fatcat:c3bzzkjwvbcblhprguedtljc6a
*the*second-*order*(polymorphic) typed lambda*calculus*, lambda abstraction over type variables leads to terms denoting polymorphic*functions*. ... We verify that some specific interpretations*of**the**calculus*proposed in*the*literature indeed yield models in our sense. ... By a further reduction*of*YY to*first*-*order*logic, which is entirely routine, one may see that*the*semantics*of*second-*order*lambda*calculus*is reducible to*first*-*order*model theory. ...##
###
Page 276 of Mathematical Reviews Vol. 47, Issue 2
[page]

1974
*
Mathematical Reviews
*

*The*section on logic contains

*the*propositional

*calculus*and

*first*

*order*logic (both with and without equality) including

*the*Henkin proof

*of*

*the*

*completeness*theorem. ... Finite sequences ¢=(I',; T',;---; T,)

*of*finite sequences

*of*formulae in a

*first*

*order*predicate language 2 are considered and called theorems

*of*

*the*system R—S

*of*

*the*predicate

*calculus*if for every i ...

##
###
Page 4 of Mathematical Reviews Vol. 13, Issue 4
[page]

1952
*
Mathematical Reviews
*

*The*four treat respectively Boolean algebra,

*the*algebra

*of*po a

*the*

*first*-

*order*predicate

*calculus*, and modal oppositional algebra. ... (Spanish) This paper contains a careful formulation

*of*

*the*classical

*first*

*order*predicate

*calculus*with identity and

*functional*(or descriptive) operations;

*the*basic propositional con- nective is

*the*...

##
###
Page 6240 of Mathematical Reviews Vol. , Issue 2001I
[page]

2001
*
Mathematical Reviews
*

*The*development

*of*fractional

*order*

*calculus*is a process

*of*com- pletion

*of*ordinary integer

*order*

*calculus*in

*the*same way as

*the*

*completion*

*of*rational numbers to reals, Riemann integral to Lebesgue ...

*The*main result

*of*this paper is that a

*functional*initiali- sation is required in

*the*fractional

*order*

*calculus*as opposed to constant initialisation in

*the*integer

*order*

*calculus*. ...

##
###
A Fractional PID Controller Based on Particle Swarm Optimization Algorithm

2020
*
Journal of Autonomous Intelligence
*

*The*fractional scale proportional-integral-differential controller is a generalization

*of*

*the*integer

*order*PID controller in

*the*complex domain. ... This paper presents a new method for

*the*design

*of*fractional PID controllers. Specifically,

*the*parameters

*of*a fractional PID controller are optimized by a particle swarm optimization algorithm. ... Based on

*the*expression

*of*higher

*order*derivatives,

*the*

*order*

*of*

*calculus*is extended from integer

*order*to fractional

*order*from

*the*classical definition

*of*

*calculus*. ...

« Previous

*Showing results 1 — 15 out of 204,255 results*