NDLI: The Solvability of the Decision Problem for Classes of Proper Formulas and Related Results

Content Provider	ACM Digital Library
Author	Di Paola, Robert A.
Copyright Year	1973
Abstract	In connection with the development of an actual question-answering system, the Relational Data File of The Rand Corporation, a class of formulas of the predicate calculus, the definite formulas of Kuhns, was proposed as the class of symbolic representations of the “reasonable” questions to put to this retrieval system. Roughly speaking, the definite formulas are those formulas $\textit{F}$ such that the set of true substitution instances of $\textit{F}$ in a finite interpretation $\textit{I}$ are preserved on passage to a certain special extension $\textit{I}′$ of $\textit{I}.$ The proper formulas are those definite formulas which are supposedly especially suitable for machine processing. It has previously been shown by the author that the decision problem for the class of definite formulas is recursively unsolvable. In this paper, however, it is shown that the decision problem for various classes of proper formulas is solvable. Thus, for each of these classes there is a mechanical procedure to decide of an arbitrary formula whether it is a member of the class. It follows that for each of these classes there is no effective transformation @@@@ which takes an arbitrary definite formula $\textit{F}$ into a proper equivalent $@@@@(\textit{F}).$ In addition, it is shown that the decision problems for a number of classes of formulas which bear a structural similarity to any class of proper formulas are recursively unsolvable.
Starting Page	112
Ending Page	126
Page Count	15
File Format	PDF
ISSN	00045411
e-ISSN	1557735X
DOI	10.1145/321738.321747
Journal	Journal of the ACM (JACM)
Volume Number	20
Issue Number	1
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1973-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Hardware and Architecture Information Systems Control and Systems Engineering Artificial Intelligence Software

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

The Recursive Unsolvability of the Decision Problem for the Class of Definite Formulas

The Solvability of the Derivability Problem for One-Normal Systems

The Solvability of the Halting Problem for 2-State Post Machines

Further Results on the Problem of Finding Minimal Length Programs for Decision Tables

Mechanical Discovery of Classes of Problem-Solving Strategies

A Class of Integration Formulas

Robustness of queuing network formulas

Recursive Formulas for the Evaluation of the Convolutions Integral

Separation of complexity classes

The Solvability of the Decision Problem for Classes of Proper Formulas and Related Results

Similar Documents

The Recursive Unsolvability of the Decision Problem for the Class of Definite Formulas

The Solvability of the Derivability Problem for One-Normal Systems

The Solvability of the Halting Problem for 2-State Post Machines

Further Results on the Problem of Finding Minimal Length Programs for Decision Tables

Mechanical Discovery of Classes of Problem-Solving Strategies

A Class of Integration Formulas

Robustness of queuing network formulas

Recursive Formulas for the Evaluation of the Convolutions Integral

Separation of complexity classes

The Solvability of the Decision Problem for Classes of Proper Formulas and Related Results