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Logical Refinements of Church's Problem [chapter]

Alexander Rabinovich, Wolfgang Thomas
Lecture Notes in Computer Science  
Extending the result of Büchi and Landweber, we present several logics L such that Church's Problem with respect to L has also a solution in L, and we discuss some perspectives of this approach.  ...  Church's Problem (1962) asks for the construction of a procedure which, given a logical specification ϕ on sequence pairs, realizes for any input sequence X an output sequence Y such that (X, Y ) satisfies  ...  Preliminaries and Main Result Church's Problem, Games, and Strategies Church's Problem deals with sequence pairs over alphabets of the form {0, 1} n .  ... 
doi:10.1007/978-3-540-74915-8_9 fatcat:3cya4d3s7zgmpocnkkvvmiuyqi

Page 1222 of Mathematical Reviews Vol. , Issue 88c [page]

1988 Mathematical Reviews  
Church’s logic of sense and denotation by regarding Church’s primitive concept relation (i.e., of one entity being a concept of another) as being always indexed by some language or other in each of its  ...  refinements of the basic proce- dure, such as constraints on framed literals and on common tails, a proper reduction refinement, a global subsumption constraint, a level subgoal reordering refinement,  ... 

Page 3958 of Mathematical Reviews Vol. , Issue 84j [page]

1984 Mathematical Reviews  
Here we study the problem of whether the corresponding conclusions change if we also take into account quantum processes (this problem was posed for Church’s thesis by G. Kreisel).  ...  Some problems of a problem-oriented expansion of Boolean functions. (Hungarian. English summary) Alkalmaz. Mat.  ... 

Page 1983 of Mathematical Reviews Vol. , Issue 90D [page]

1990 Mathematical Reviews  
logic into formulas of modal logic [cf.  ...  Capitalizing on work of Woods, who showed that if Problem 2 has a positive solution then Problem | also has a positive solu- tion [“Some problems in logic and number theory and their con- nections”, Ph.D  ... 

Page 4124 of Mathematical Reviews Vol. , Issue 82j [page]

1982 Mathematical Reviews  
This problem “helps us understand some of the most striking features of [Russell’s] thought in 1905-1914” (p. 172).  ...  The author defends the view that the cogency of the alleged evidence for Church’s thesis (as modified!)  ... 

Proof of Church's Thesis [article]

Ramón Casares
2016 arXiv   pre-print
We prove that if our calculating capability is limited to that of a universal Turing machine with a finite tape, then Church's thesis is true. This way we accomplish Post (1936) program.  ...  of symbolic logics of a certain general type and Church's results on the recursive unsolvability of certain problems be transformed into conclusions concerning all symbolic logics and all methods of solvability  ...  a small enough part of any computation, persons can calculate if it is computed rightly or wrongly.§8Conclusions¶1• We can summarize thesis 2 and thesis 3 in a refined Church's thesis: What is effectively  ... 
arXiv:1209.5036v5 fatcat:7jrv2vyzn5ctrhy4afmrphnzem

Page 1042 of Mathematical Reviews Vol. , Issue 92b [page]

1992 Mathematical Reviews  
Important re- sults on the undecidability of predicate logic and Church’s thesis are presented in the first two chapters.  ...  Chapter 4 treats various types of logics of this type, namely the logic of revisable reasoning, nonmonotonic logic, default logic, McDermott’s nonmonotonic logic, modal logic of knowledge and belief, and  ... 

Page 294 of The American Ecclesiastical Review Vol. 104, Issue 4 [page]

1941 The American Ecclesiastical Review  
Such a form of logical procedure would of necessity demand that the initial step toward solution must aD  ...  of the problem, one cannot fail to observe the practically unanimous appeal to a deductive system of methodology.  ... 

Page 4624 of Mathematical Reviews Vol. , Issue 2002G [page]

2002 Mathematical Reviews  
We show that the validity problem for such a logic is not recursively enumerable, hence FO-LTL™ is not recursively axiomatizable.  ...  approximation: a refined model construction for various lambda calculi” [Theoret.  ... 

Proof of Church's Thesis

Ramón Casares
2017 Figshare  
We prove that if our calculating capability is limited to that of a universal Turing machine with a finite tape, then Church's thesis is true. This way we accomplish Post (1936) program.  ...  of symbolic logics of a certain general type and Church's results on the recursive unsolvability of certain problems be transformed into conclusions concerning all symbolic logics and all methods of solvability  ...  www.ramoncasares.com 20170430 PoCT 5 §8 Conclusions ¶1 · We can summarize thesis 2 and thesis 3 in a refined Church's thesis: ⋄ Thesis 6 What is effectively calculable is effectively computable. ¶2 ·  ... 
doi:10.6084/m9.figshare.4955501.v1 fatcat:cna3fmjivbcnjpimvyq6q5qjcq

Proof of Church's Thesis

Ramón Casares
2022 figshare.com  
We prove that if our calculating capability is that of a universal Turing machine with a finite tape, then Church's thesis is true. This way we accomplish Post (1936) program.  ...  of symbolic logics of a certain general type and Church's results on the recursive unsolvability of certain problems be transformed into conclusions concerning all symbolic logics and all methods of solvability  ...  So, taking a small enough part of any computation, we can calculate whether it is computed rightly or wrongly. §8 Conclusions ¶1 • We can summarize thesis 2 and thesis 3 in a refined Church's thesis: What  ... 
doi:10.6084/m9.figshare.4955501.v3 fatcat:tyuelale5fahfmfdx7mbxj7e2e

Dependent Event Types [chapter]

Zhaohui Luo, Sergei Soloviev
2017 Lecture Notes in Computer Science  
As an example of applications, it is shown that dependent event types give a natural solution to the incompatibility problem (sometimes called the event quantification problem) in combining event semantics  ...  This paper studies how dependent types can be employed for a refined treatment of event types, offering a nice improvement to Davidson's event semantics.  ...  Its proof is based on the embedding of Church's simple type theory into the calculus of constructions [10] .  ... 
doi:10.1007/978-3-662-55386-2_15 fatcat:4vbcndrt4bgalgdoozr2scqaha

Page 745 of Mathematical Reviews Vol. 53, Issue 3 [page]

1977 Mathematical Reviews  
Say that a logic LZ, is canonical if the frame of its canonical model is a frame for L, and that L is natural if the frame of every model for Z that is refined in the sense of S. K.  ...  But this is perhaps the first time that the tools of classical model theory have been applied in a Organized manner to problems in modal propositional logic. ie paper may well open up a new avenue of research  ... 

Page 424 of Mathematical Reviews Vol. , Issue 85b [page]

1985 Mathematical Reviews  
How does it relate to the reviewer’s uncited refine- ments [International logic colloquium (Clermont-Ferrand, 1975), 167-181, CNRS, Paris, 1977; MR 80g:03057|?  ...  Logic, methodology and philosophy of science, VI (Hannover, 1979), pp. 141-143, Stud. Logic Foundations Math., 104, North-Holland, Amsterdam-New York, 1982.  ... 

Page 235 of Interpretation Vol. 23, Issue 2 [page]

1969 Interpretation  
Because the church does not possess either sufficient or firmly established imagery, the theologian is thrust into the historical problems of the emergence of symbols.  ...  He cannot be limited to interpretation and correlation of existing imagina- tive comparisons, for he is responsible for serving in the church’s continuing process of symbol formation.  ... 
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