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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  ... 

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, ---).  ... 

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).  ... 

Representing von Neumann–Morgenstern Games in the Situation Calculus

Oliver Schulte, James Delgrande
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 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  ... 
doi:10.1023/b:amai.0000034523.18162.6b fatcat:3f7qb2trovcfnbptdhv4hcvjty

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

Walter DEAN
2017 Annals of the Japan Association for Philosophy of Science  
He also showed that if all 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  ... 
doi:10.4288/jafpos.25.0_45 fatcat:hdjy6zyp2ra7vlr4pwr4bg52fe

Book Review: Mathematical logic

Hartley Rogers Jr.
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  ... 
doi:10.1090/s0002-9904-1958-10141-x fatcat:ylfurhlhincjxbmbntus4scamy

Ten problems in Gödel logic

Juan P. Aguilera, Matthias Baaz
2016 Soft Computing - A Fusion of Foundations, Methodologies and Applications  
Preliminaries Gödel logics are extensions 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.  ... 
doi:10.1007/s00500-016-2366-9 pmid:32355463 pmcid:PMC7175704 fatcat:fsbpy665y5ai3pcffvbn7khq2i

FROM STENIUS' CONSISTENCY PROOF TO SCHÜTTE'S CUT ELIMINATION FOR ω-ARITHMETIC

ANNIKA SIDERS
2015 The Review of Symbolic Logic  
Based on this reduction condition Stenius proves that 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.  ... 
doi:10.1017/s1755020315000337 fatcat:undhkrpgwbeyxppprpvrjp6gh4
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