Intelligent System for Predicting the Feasibility of Using Computed Tomography

Abstract

This article describes the principles of creating an intelligent system using a JSM method of automated research support (JSM method ARS) to predict the feasibility of computed tomography application. The procedures of JSM research that are adopted to increase the reliability of the empirical regularities obtained in the system are described. The obtained empirical regularities and their expert ratings are given.

APPENDICES

Appendix 1. Similarity Predicate Definitions

$M_{{a,n}}^{\sigma }(V,W)$ (σ = +, –, 0, τ)| are minimal predicates that implement inductive inferences. They can be supplemented with more informative improvements²⁶

Ban on counterexamples:

${{(b)}^{ + }}\,\,\forall \,\,X\,\,\forall \,\,Y(((\begin{array}{*{20}{c}} V&X \end{array})\& {\text{(}}\begin{array}{*{20}{c}} W&Y \end{array})) \to$$\to ({{J}_{{(1,n{\text{)}}}}}(X \Rightarrow \,{{\,}_{1}}Y) \vee {{J}_{{(\tau ,n)}}}(X \Rightarrow \,{{\,}_{1}}Y))),$${{{\text{(}}b)}^{ + }}\,\,\forall \,\,X\,\,\forall \,\,Y(((\begin{array}{*{20}{c}} V&X \end{array})\& {\text{(}}\begin{array}{*{20}{c}} W&Y \end{array})) \to$ $\to ({{J}_{{( - 1,n{\text{)}}}}}(X \Rightarrow \,{{\,}_{1}}Y) \vee {{J}_{{(\tau ,n)}}}(X \Rightarrow \,{{\,}_{1}}Y))),$

$M_{{ab,n}}^{ + }(V,W)\,\,\,\mathop \to \limits^ \leftarrow {\kern 1pt} M_{{a,n}}^{ + }(V,W)\& {{(b)}^{ + }},$ $M_{{ab,n}}^{ - }(V,W)\mathop \to \limits^ \leftarrow {\kern 1pt} {\kern 1pt} M_{{a,n}}^{ - }(V,W)\& {{(b)}^{ - }},$

Method of difference:

${{({{d}_{0}})}^{ + }}\,\,\forall \,\,X\,\,\forall \,\,Y\,\,\forall \,\,Z\,\,\forall \,\,U(({{J}_{{(1,n{\text{)}}}}}(X \Rightarrow \,{{\,}_{1}}Y)$ $\& (W\,\,Y)\& (V\,\,X)\& ((X\,\, - V)\,\,Z)$ $\& ((X\,\, - V) \ne \emptyset )\& \neg (V\,\,Z)) \to$ $\to \neg {{J}_{{{\text{(1}}{\text{,n)}}}}}(Z \Rightarrow \,{{\,}_{1}}U) \vee \neg (W\,\,U))){{,}^{6}}$

${{({{d}_{0}})}^{ - }}\,\,\forall \,\,X\,\,\forall \,\,Y\,\,\forall \,\,Z\,\,\forall \,\,U(({{J}_{{( - 1,n{\text{)}}}}}(X \Rightarrow \,{{\,}_{1}}Y)$ $\& (W\,\,Y)\& (V\,\,X)\& ((X\,\, - V)\,\,Z)$ $\& ((X\,\, - V) \ne \emptyset )\& \neg (V\,\,Z)) \to$$\to \neg {{J}_{{{\text{(}} - {\text{1}}{\text{,}}n{\text{)}}}}}(Z \Rightarrow \,{{\,}_{1}}U) \vee \neg (\begin{array}{*{20}{c}} W&U \end{array}))),$

$M_{{ad0,n}}^{ + }(V,W)\,\,\, \leftarrow \to {\kern 1pt} M_{{a,n}}^{ + }(V,W)\& {{({{d}_{0}})}^{ + }},$ $M_{{ad0,n}}^{ - }(V,W)\,\,\, \leftarrow \to {\kern 1pt} M_{{a,n}}^{ - }(V,W)\& {{({{d}_{0}})}^{ - }}.$

Method of difference with a ban on counterexamples:

$M_{{ad0b,n}}^{ + }(V,W)\,\,\, \leftarrow \to {\kern 1pt} M_{{a,n}}^{ + }(V,W)\& {{(b)}^{ + }}\& {{({{d}_{0}})}^{ + }},$ $M_{{ad0b,n}}^{ - }(V,W)\,\,\, \leftarrow \to {\kern 1pt} M_{{a,n}}^{ - }(V,W)\& {{(b)}^{ - }}\& {{({{d}_{0}})}^{ - }}.$

Appendix 2. List of Regularities Obtained

Signs and abbreviations:

• Ages are divided into decades: 3: 30–39, 4: 40–49, 5: 50–59, 6: 60–69, 7: 70–79, 8: 80–89;

• Alcohol (alcohol addiction) only has yes or no values;

• Tobacco smoking (tobacco addiction) only has yes or no values;

• Body mass index (BMI) has the following values: Below: below the norm, Norm: normal, Above: above the norm;

• The duration of the disease was compared across key points: 1 year, 2 years, 3 years, 5 years;

• Pain (severity of pain) has the possible values yes (severe pain) and no (mild pain);

• Diabetes mellitus (DM) only has yes or no values.

k is the number of “parents” of the hypothesis (examples that generate it).

If the corresponding regularity is generated by several strategies, the largest one was chosen (since the strategies by which the regularities were obtained in our experiments turned out to be comparable). Thus, each empirical regularity was assigned one rating.

Experiment 1. Positive regularities
〈b, Strab,ab〉
#	Age (decade)	Alcohol addiction	Tobacco smoking	BMI	Duration	Pain > 6 (Strong)	DM	k	Expert’s rating
2105				Norm	<3 Years	Yes		17	3
2168		No			<3 Years	Yes		16	3
132			No		<2 Years	Yes		13	3
205					<1 Years	Yes		12	3
2114	5				<3 Years	Yes		6	3
3145		No	No		From 1 to 2 years			6	3
3321	6				<2 Years	Yes		6	3
2178	5	No		Norm		Yes		5	3
2538	5	No				Yes	No	4	3
2548	5		Yes		<3 Years		No	4	3
3028	5				From 1 to 3 years		No	4	3
3314	6	Yes			<5 Years		No	4	3
3315		Yes			<1 Years		No	4	3
9		Yes	No		<5 Years	Yes	No	3	3
1520	5			Norm		Yes	Yes	3	3
〈b, Strab,abd0〉
#	Age (decade)	Alcohol addiction	Tobacco smoking	BMI	Duration	Pain > 6 (Strong)	DM	k	Expert’s rating
1537	5	No				Yes
〈a, Strab,ab〉
#	Age (decade)	Alcohol addiction	Tobacco smoking	BMI	Duration	Pain > 6 (Strong)	DM	k	Expert’s rating
33				Norm		Yes		23	3
689				Norm	<2 Years			19	2
207		No			<2 Years			18	3
1089			No			Yes		18	2
1280		No			<5 Years	Yes		17	2
1832			No		<2 Years			16	3
1267		No				Yes	No	15	2
1837					<1 Years			14	3
795	5				<5 Years			9	2
794		Yes		Norm	<5 Years			8	2
1178	6				<5 Years	Yes		8	3
1428	5						No	8	2
2120					>2 Years	Yes	No	8	1
3618	6				<3 Years		No	8	2
1834	6		No		<5 Years		No	7	3
1644		Yes	No				No	6	2
2552		No	Yes		<3 Years			6	3
3609	6			Norm	<3 Years			6	3
69			No	Above			No	5	2
681	5		Yes	Norm				5	3
3411	4		Yes		>1 Years		No	5	1
2276		No		Above			No	4	1
3314	6	Yes			<5 Years		No	4	2
3424	4	Yes			>1 Years			4	1
〈n, Strab,abd0〉
#	Age (decade)	Alcohol addiction	Tobacco smoking	BMI	Duration	Pain > 6 (Strong)	DM	k	Expert’s rating
23073	6		Yes		From 2 to 5 years		No	3	2
〈a, Strab,abd0〉
#	Age (decade)	Alcohol addiction	Tobacco smoking	BMI	Duration	Pain > 6	DM	k	Expert’s rating
694				Norm	<5 Years			23	1
1265		No				Yes		21	2
257		No			<5 Years			20	2
4			No				No	19	1
802			No		<5 Years			19	2
2744		No	No	Norm				11	1
1843	6				<5 Years		No	10	2
2103					>2 Years	Yes		10	1
76	5					Yes		8	2
54	5		Yes					7	2
1274	4				>1 Years		No	6	1
2154					From 2 to 5 years		No	5	1
478		Yes		Above	>3 Years			4	2
3424	4	Yes			>1 Years			4	2
1724				Above	>3 Years		No	3	2
1286	4		No		>1 Years			2	2
Experiment 1. Negative regularities
〈a, Strabd0,a〉
#	Age (decade)	Alcohol addiction	Tobacco smoking	BMI	Duration	Pain > 6	DM	k	Expert’s rating
69	3				>3 Years			7	2
353			No		>3 Years			7	2
269					>1 Years	No	Yes	6	3
546		No			>5 Years	No		6	3
308	5					No		3	3
399	4			Norm	>5 Years		Yes	3	2
267	6			Above	>1 Years	No		2	3
480	6		Yes		From 1 to 2 years	No		2	3
672	4	No	Yes	Norm	>2 Years			2	2
Experiment 1. Negative hypotheses that are not regularities
〈Strab,ad0〉
#	Age (decade)	Alcohol addiction	Tobacco smoking	BMI	Duration	Pain > 6	DM	k	Expert’s rating
271					>1 Years			69	3
〈Strab,a〉
#	Age (decade)	Alcohol addiction	Tobacco smoking	BMI	Duration	Pain > 6	DM	k	Expert’s rating
62						No		70	2
224							No	51	1
4097				Norm				47	1
4100			Yes					45	1
364					<5 Years			33	1
4108		Yes						33	1
1249				Above				25	1
1879				Below				8	1
Experiment 2. Positive regularities
〈a, Strab,ab〉
#	Age (decade)	Alcohol addiction	Tobacco smoking	BMI	Duration	Pain > 6	DM	k	Expert’s rating	Present in experiment 1
3315		Yes			<1 Years		No	4	3	Yes
〈a, Stra,ab〉
#	Age (decade)	Alcohol addiction	Tobacco smoking	BMI	Duration	Pain > 6	DM	k	Expert’s rating	Present in experiment 1
884		No		Norm				20	2	No
1103			No	Norm				15	2	No
2520		No	Yes					13	2	No
2101		No			>2 Years			12	2	No
1835				Norm	<1 Years			11	3	No
4010		No					Yes	9	2	No
1857	6			Norm	<5 Years			8	3	No
2728				Norm	<2 Years		Yes	8	2	No
1830		Yes			<1 Years			6	3	No
〈a, Strab,abd0〉
#	Age (decade)	Alcohol addiction	Tobacco smoking	BMI	Duration	Pain > 6	DM	k	Expert’s rating	Present in experiment 1
3145		No	No		From 1 to 2 years			6	3	Yes
3315		Yes			<1 Years		No	4	3	Yes
〈n, Strab,abd0〉
#	Age (decade)	Alcohol addiction	Tobacco smoking	BMI	Duration	Pain > 6	DM	k	Expert’s rating	Present in experiment 1
23055	5		No	Below	>1 Years			3	2	No
〈n, Stra,abd0〉
#	Age (decade)	Alcohol addiction	Tobacco smoking	BMI	Duration	Pain > 6	DM	k	Expert’s rating	Present in experiment 1
37		No			>1 Years			22	2	No
75	5							14	1	No
121			No		>1 Years			14	1	No
494							Yes	14	2	No
2520		No	Years					13	2	No
1855	6				<5 Years			12	3	No
486				Above				11	1	No
998		Yes	No					7	1	No
601	3	Yes		Norm				5	1	No
Experiment 2. Negative regularities
〈a, Strabd0,a〉
#	Age (decade)	Alcohol addiction	Tobacco smoking	BMI	Duration	Pain > 6	DM	k	Expert’s rating	Present in experiment 1
473				Norm			No	7	3	No
474			Yes				No	8	3	No
479			Yes		<5 Years	No		6	2	No

Appendix 3. List of Correct Predictions and Errors by Strategies for the Last Expansion

For experiment 1.
	10	а	b	с
	+	-	+	-	+	-	+	-
Strab,ab	8	3		3	2	1	1	2
Stra,abd0	11			9
Strab,bd0	10			4			1	5
Stra,ab	9			5	2	4
Strad0,ad0		9	5		3		3
Strabd0,ad0		9	8				3
Strad0,a		9	8		3
Strabd0,a		9	11
Strab,ad0	3	5	1		7	4
Strad0,ab	2	4	1		1		7	5
Strab,a		5	1		10	4
Strabd0,ab		4	2				9	5
Strad0,abd0	3						8	9
Stra,ad0	3				8	9
Strabd0,abd0							11	9
Stra,a					11	9
For experiment 2.
	10	а	b	с
	+	-	+	-	+	-	+	-
Stra,abd0	7			3
Strab,abd0	5						2	3
Strab,ab	4	1	1		1		1	2
Stra,ab	5			2	2	1
Strab,ad0	2	2			3	2		1
Strab,a		3	2		5
Strad0,a, Strabd0,a		3	7
Stra,ad0	2			1	5			2
Strad0,ad0, Strabd0,ad0		2	5				2	1
Strad0,ab, Strabd0,ab		1	2				5	2
Strad0,abd0, Strabd0,abd0							7	3
Stra,a					7	3