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### Page 626 of Mathematical Reviews Vol. 20, Issue 6 [page]

1959 Mathematical Reviews
The author proposes the following definitions of a non- relativised (I) notion of correctness of inductive inference and two versions (II.1 and II.2) of a relativised notion of correctness of inductive  ...  On “good” and “bad” induction. (Polish. Russian and Studia Logica 5 (1957), 43-70.  ...

### Complete and easy bidirectional typechecking for higher-rank polymorphism

Jana Dunfield, Neelakantan R. Krishnaswami
2013 Proceedings of the 18th ACM SIGPLAN international conference on Functional programming - ICFP '13
Bidirectional typechecking, in which terms either synthesize a type or are checked against a known type, has become popular for its scalability (unlike Damas-Milner type inference, bidirectional typing  ...  We give an algorithm for implementing the declarative system; our algorithm is remarkably simple and well-behaved, despite being both sound and complete.  ...  By inversion, τ 1 = τ 11 → τ 12 and τ 2 = τ 21 → τ 22 . Therefore, we have monotypes in the first and second premises. By induction on the first premise, |unsolved(Θ)| ≤ |unsolved(Γ )|.  ...

### Complete and easy bidirectional typechecking for higher-rank polymorphism

Jana Dunfield, Neelakantan R. Krishnaswami
2013 SIGPLAN notices
Bidirectional typechecking, in which terms either synthesize a type or are checked against a known type, has become popular for its scalability (unlike Damas-Milner type inference, bidirectional typing  ...  We give an algorithm for implementing the declarative system; our algorithm is remarkably simple and well-behaved, despite being both sound and complete.  ...  By inversion, τ 1 = τ 11 → τ 12 and τ 2 = τ 21 → τ 22 . Therefore, we have monotypes in the first and second premises. By induction on the first premise, |unsolved(Θ)| ≤ |unsolved(Γ )|.  ...

### Abstracts of papers

1960 Journal of Symbolic Logic (JSL)
The rules of inference of M are: (i) from h H and h H -*• 0 to infer |-0, provided H is closed or 0 is open; (ii) from h H to infer b H\xjy\; (iii) from \-H -»• 0 to infer \-AxH ->• 0, provided 0 is open  ...  Independence of induction schema in recursive arithmetic.  ...

### Complete and Easy Bidirectional Typechecking for Higher-Rank Polymorphism [article]

Jana Dunfield, Neelakantan R. Krishnaswami
2020 arXiv   pre-print
Bidirectional typechecking, in which terms either synthesize a type or are checked against a known type, has become popular for its scalability (unlike Damas-Milner type inference, bidirectional typing  ...  We give an algorithm for implementing the declarative system; our algorithm is remarkably simple and well-behaved, despite being both sound and complete.  ...  Therefore, we have monotypes in the first and second premises. By induction on the first premise, |unsolved(Θ)| ≤ |unsolved(Γ )|. By induction on the second premise, |unsolved(∆)| ≤ |unsolved(Θ)|.  ...

### Iterated Limiting Recursion and the Program Minimization Problem

L. K. Schubert
1974 Journal of the ACM
KEY WORDS AND PHRASES: function identification, minimal programs, limiting recursion, inductive inference, program length measures, program properties, degree of unsolvability. 1.  ...  Intuitively, iterated limiting identification might be regarded as higher-order inductive inference performed collectively by an ever growing community of lower-order inductive inference Session 18 Automatic  ...  Indeed, the Finally, the point is emphasized in the use of small programs for inductive inference concluding remarks that limiting recursively is a recurring theme in the literature (see solvable  ...

### Some psychophysiological and latency correlates of rule induction

Marjorie F. Elias, Sheldon H. White
1969 Psychonomic Science
) the difference in decrease between solved and unsolved tasks M-YlS significant for SP and RL butnotfor Vc.  ...  Comparing early and late measures on solved and unsolved tasks, it was found that: ( 1) response decrements did occur in all three measures in solved tasks; (2) they did not occur in unsolved tasks; (3  ...  ) the difference in decrease between solved and unsolved tasks M-YlS significant for SP and RL butnotfor Vc.  ...

### Page 3996 of Mathematical Reviews Vol. , Issue 83j [page]

1983 Mathematical Reviews
Authors’ summary: “Recent results in the theory of inductive inference are summarized.  ...  , uniform inference, and inference of nonrandom sequences.  ...

### Page 10 of Journal of Political Economy Vol. 48, Issue 1 [page]

1940 Journal of Political Economy
The question as to the primary or immediate data of consciousness is perhaps the main perennial, unsolved and probably unsolvable problem of the the- ory of knowledge as a whole. What is observation?  ...  and What is inference? are questions on a par with What is truth? if they do not simply restate the same question.  ...

### Functional neuroanatomy of learned helplessness

Herbert Bauer, Jürgen Pripfl, Claus Lamm, Christoph Prainsack, Nadia Taylor
2003 NeuroImage
processing unsolvable tasks.  ...  Cortical LORETA (Pascual-Marqui, 1999) of SCP topographies (Bauer, 1998; Bauer et al., 2000) and subsequent statistical nonparametric mapping (SnPM; Nichols and Holmes, 2002) analysis indicate clear reduction  ...  of control ("Induction")], items 1-25 ("Induction1"), items 26 -50 ("Induction 2"), of all unsolvable items [withdrawal of control ("Withdrawal")], of unsolvable items among trials 51-80 ("Withdrawal  ...

### Page 4463 of Mathematical Reviews Vol. , Issue 82j [page]

1982 Mathematical Reviews
Fundamental concepts and assumptions of the proposed formalization are described. Interpretations of a general training scheme and of the induction inference model are discussed.”  ...  Training .as a variety of induction inference. Izv. Akad. Nauk SSSR Tehn. Kibernet. 1978, no. 3, 62-69 ( Russian); translated as Engrg. Cybernetics 16 (1978), no. 3, 46-52.  ...

### Kind inference for datatypes

Ningning Xie, Richard A. Eisenberg, Bruno C. d. S. Oliveira
2019 Proceedings of the ACM on Programming Languages (PACMPL)
With these features, the challenge of kind inference for datatype declarations has presented itself and become a worthy research problem on its own. This paper studies kind inference for datatypes.  ...  This work can serve as a guide both to language designers who wish to formalize their datatype declarations and also to implementors keen to have principled inference of principal types.  ...  Kind Inference for Datatypes: Technical Supplement 53:3 B.1 Constraint-Based Type Inference Type inference in GHC is based on generating and solving constraints [Pottier and Rémy 2005; Vytiniotis et  ...

### Intersection and Singleton Type Assignment Characterizing Finite Böhm-Trees

Toshihiko Kurata
2002 Information and Computation
Intersection types and type constants representing unsolvability and singleton sets of λ-terms are incorporated into the Curry version of a simple type assignment system.  ...  In our system, instead of the refinement of ω, we use intersection types, type constants representing unsolvability, and singleton types.  ...  For a basis , a λ-term M and a type A, the judgment M : A is generated by the following natural deduction style axioms and inference rules: (var) x : A if x : A ∈ ( ) M : if M is unsolvable (→I) , x :  ...

### Page 4 of The Hibbert Journal : A Quarterly Review of Religion, Theology and Philosophy Vol. 10, Issue 1 [page]

1911 The Hibbert Journal : A Quarterly Review of Religion, Theology and Philosophy
the last word on empirical inference, stared helplessly at its difficulties through two volumes of logic, and left them unsolved at the end.  ...  The question as to what exactly is given in immediate experience, and by what logical or inductive process anything can be inferred from it, the nature of causation, the grounds of our conviction that  ...

### Navigating through the Frame Problem: Review of Reasoning Agents in a Dynamic World

Selmer Bringsjord, Christopher A. Welty
1994 The AI Magazine
The idea is that although an AI system without the frame problem might, say, read an echocardiogram and diagnose a heart defect, a really smart autonomous robot will arrive only if, like us humans, it  ...  However, if Hayes is correct that causal laws can't be known, it follows that the induction problem is unsolvable. It then follows, by modus tollens, that the frame problem itself is unsolvable!  ...  If such is the case, and others (for example, van Brakel [1992] ) seem to think it is, we're still left with the contrapositive of Fetzer's conditional: If the induction problem is unsolvable (as Hayes  ...
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