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Page 465 of Mathematical Reviews Vol. 27, Issue 3
[page]

1964
*
Mathematical Reviews
*

*The*author simplifies Wang’s

*calculus*

*of*partial

*predicates*by finitely

*axiomatizing*

*the*corresponding propositional

*calculus*. ...

*The*author investigates generalizations

*of*first-order

*predicate*

*calculus*(without identity) obtained by intro- ducing

*predicates*and functions with

*infinitely*many argu- ment places and admitting quantifiers ...

##
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Page 5 of Mathematical Reviews Vol. 26, Issue 4
[page]

1963
*
Mathematical Reviews
*

Nakamura, Akira 3592 On an

*axiomatic*system*of**the**infinitely*many-*valued*threshold logics. Z. Math. Logik Grundlagen Math. 8 (1962), 71-76. ...*The*author extends*the*results*of*a previous paper [#3592] to an*infinite*-*valued*logic whose truth-*values*are all*infinite*ordered sequences (71, X2, - --) such that 2; € ees » I (i=1, 2, ---). ...##
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Page 5020 of Mathematical Reviews Vol. , Issue 2001G
[page]

2001
*
Mathematical Reviews
*

To computations,

*predicates*can be introduced, leading to a*predicate*algebra*of*computations if*the*classical operators*of**predicate*logic are lifted to those*predicates*. ... Computation*calculus*is an abstract operational semantics in terms*of*finite and*infinite*sequences*of*states. This is how computations are represented. ...##
###
Page 6167 of Mathematical Reviews Vol. , Issue 94k
[page]

1994
*
Mathematical Reviews
*

*The*author considers a logical system LS obtained as a restric- tion

*of*a multiset

*calculus*for

*the*classical first-order

*predicate*logic by omitting

*the*structural contraction rule, and describes

*the*...

*value*when one

*of*its arguments is undefined). ...

##
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Representing von Neumann–Morgenstern Games in the Situation Calculus

2004
*
Annals of Mathematics and Artificial Intelligence
*

We show that sequential VM games with countably many actions and continuous utility functions have a sound and complete

doi:10.1023/b:amai.0000034523.18162.6b
fatcat:3f7qb2trovcfnbptdhv4hcvjty
*axiomatization*in*the*situation*calculus*. ... We discuss*the*application*of*various concepts from VM game theory to*the*theory*of*planning and multi-agent interactions, such as representing concurrent actions and using*the*Baire topology to define ... Previous versions were presented at JAIST (Japanese Advanced Institute for Science and Technology),*the*2001 Game Theory and Epistemic Logic Workshop at*the*University*of*Tsukuba, and*the*AI group at*the*...##
###
Page 4293 of Mathematical Reviews Vol. , Issue 94h
[page]

1994
*
Mathematical Reviews
*

*The*Lukasiewicz three-

*valued*

*calculus*became

*the*starting point for

*the*construction

*of*finitely many-

*valued*logics, as well as for systems with an

*infinite*number

*of*logical

*values*, and

*the*variety

*of*...

*The*many-

*valued*first-order

*predicate*calculi

*of*Post are specifically studied. ...

##
###
Page 4444 of Mathematical Reviews Vol. , Issue 95h
[page]

1995
*
Mathematical Reviews
*

*The*book begins by presenting, in a standard way,

*the*funda- mentals

*of*

*the*elementary classical logic, its algebraization and

*the*first-order

*predicate*

*calculus*. ... Rosser and Turquette’s well-known work on a general method

*of*

*axiomatization*

*of*finitely many-

*valued*systems, and also

*the*question

*of*their extension to

*predicate*logic, by dealing with con- nectives ...

##
###
Page 23 of Mathematical Reviews Vol. , Issue 2000a
[page]

2000
*
Mathematical Reviews
*

*The*author also discusses

*the*difficulties

*of*directly extending such an approach to

*infinite*-

*valued*logics (due, in rough terms, to

*the*impossibility

*of*obtaining first-order

*axiomatizations*for

*infinite*-

*valued*... sequent

*calculus*, by several authors (and

*the*paper provides references for all

*of*them). ...

##
###
Page 112 of Mathematical Reviews Vol. 19, Issue 2
[page]

1958
*
Mathematical Reviews
*

In

*the**axiomatic*version,*the*concept*of*a polyadic algebra takes*the*place*of*an (applied) lower*predicate**calculus*. ... This paper represents*the*culmination*of**the*author's work on*the*algebraic-*axiomatic*version*of**the*lower*predicate**calculus*. ...##
###
Page 15 of Mathematical Reviews Vol. 56, Issue 1
[page]

1978
*
Mathematical Reviews
*

*The*w*-

*valued*

*predicate*

*calculus*was introduced by H. Rasiowa [Bull. Acad. Polon Sci. Sér. Sci. Math. Astronom. ...

*The*author takes into consideration

*the*sentential

*calculus*W and its

*axiomatic*version W,. ...

##
###
Page 1408 of Mathematical Reviews Vol. 51, Issue 5
[page]

1976
*
Mathematical Reviews
*

This paper consists

*of*three parts, namely, an*infinite*-*valued*proposi- tional*calculus*, an approximate*predicate**calculus*and an inter pretation*of**the*approximate*predicate**calculus*. ... Different formulations*of**the**infinite*-*valued*propositional*calculus*are outlined and investigated. A notion*of*approximate*predicate**calculus*is obtained. Interpretations are defined. ...##
###
Bernays and the Completeness Theorem

2017
*
Annals of the Japan Association for Philosophy of Science
*

He also showed that if all

doi:10.4288/jafpos.25.0_45
fatcat:hdjy6zyp2ra7vlr4pwr4bg52fe
*of**the*A i are irrefutable in*the*propositional*calculus*, then F is irrefutable in*the**predicate**calculus*. ...*of*deductive closure*of**the**predicate**calculus*, only under*the*assumption*of**the*consistency*of**the*number-theoretic formalism . . . ¶ This consideration indicates that*the*task*of*a proof*of**the*consistency ...##
###
Book Review: Mathematical logic

1958
*
Bulletin of the American Mathematical Society
*

*The*Heyting intuitionist system is given. Chapter II (16 pp.) on (lower)

*predicate*

*calculus*, gives both an

*axiomatic*formulation with deduction theorem and Quine's natural inference formulation. ...

*The*Russell-Whitehead

*axiomatization*is then described and a deduction theorem outlined. ...

*The*author himself falls victim to this when he sets up what appears to be a

*predicate*

*calculus*with

*infinitely*many axioms (there is no

*predicate*substitution rule) and then on several later occasions ...

##
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Ten problems in Gödel logic

2016
*
Soft Computing - A Fusion of Foundations, Methodologies and Applications
*

Preliminaries Gödel logics are extensions

doi:10.1007/s00500-016-2366-9
pmid:32355463
pmcid:PMC7175704
fatcat:fsbpy665y5ai3pcffvbn7khq2i
*of*intuitionistic logic that take truth*values*in a closed subset*of**the*interval [0, 1]. We denote by G V*the*Gödel logic whose truth-*value*set is V . ... Definition 1 A valuation I for*the*Gödel logic G V is 1. a nonempty set U = U I ,*the*'universe'*of*I, 2. for each k-ary*predicate*symbol P, a function P I : U k ... Compliance with ethical standards Conflict*of*interest*The*authors declare that they have no conflict*of*interest. ...##
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FROM STENIUS' CONSISTENCY PROOF TO SCHÜTTE'S CUT ELIMINATION FOR ω-ARITHMETIC

2015
*
The Review of Symbolic Logic
*

Based on this reduction condition Stenius proves that

doi:10.1017/s1755020315000337
fatcat:undhkrpgwbeyxppprpvrjp6gh4
*the*complexity*of*formulas in a derivation can be limited by*the*complexity*of**the*conclusion. ... based on invertibility*of**the*logical rules. ...*calculus*system and*the**axiomatic*system*The**axiomatic*system Z ax and*the*sequent*calculus*system Z sc are equivalent. 3.2 Theorem. ...
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