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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

Asta Halkjær From, Alexander Birch Jensen, Anders Schlichtkrull, Jørgen Villadsen
2020 Electronic Proceedings in Theoretical Computer Science  
We present soundness and 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.  ... 
doi:10.4204/eptcs.313.5 fatcat:6mjb5dae3beizfqa2ncyjtmo4y

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]

Michael Beeson
2004 Lecture Notes in Computer Science  
Lambda logic is 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.  ... 
doi:10.1007/978-3-540-25984-8_34 fatcat:vqfgfabukfhbdb6fp6ugxz45ka

Superposition with First-class Booleans and Inprocessing Clausification [chapter]

Visa Nummelin, Alexander Bentkamp, Sophie Tourret, Petar Vukmirović
2021 Lecture Notes in Computer Science  
AbstractWe present a 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.  ... 
doi:10.1007/978-3-030-79876-5_22 fatcat:ndddytox3vcefnvnk6xvglqyhi

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]

Ahmed Bhayat, Giles Reger
2020 Lecture Notes in Computer Science  
We present a refutationally 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.  ... 
doi:10.1007/978-3-030-51074-9_16 fatcat:tw3vp2xhnffo7m7gv5ymma4c2a

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]

Richard Zach
2006 Lecture Notes in Computer Science  
In particular, Gödel's 1931 paper on incompleteness and 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.  ... 
doi:10.1007/11780342_59 fatcat:mi2qey4monflhagqyijp3wqjfi

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

Kim B. Bruce, Albert R. Meyer, John C. Mitchell
1990 Information and Computation  
In 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.  ... 
doi:10.1016/0890-5401(90)90044-i fatcat:c3bzzkjwvbcblhprguedtljc6a

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

Yinglei Song
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.  ... 
doi:10.32629/jai.v3i1.94 fatcat:qdqbdyvh75dclo5bx2a2hxgndu
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