# rational number: be closed under multiplication

from Quasimodo

## Related concepts

 Parents numberWeight: 0.73, real numberWeight: 0.63, problemWeight: 0.62, objectWeight: 0.55 Siblings irrational numberWeight: 0.82, integerWeight: 0.60, complex numberWeight: 0.38, imaginary numberWeight: 0.38, social security numberWeight: 0.37

## Related properties

 Similarity Property be closed under multiplication 1.00 be closed under subtraction 0.81 be closed under division 0.77 be closed in subtraction 0.76 be closed under addition 0.76

## Clauses

### Plausibility inference from child typicality

0.61
Rule weight: 0.66
Evidence weight: 0.92
Similarity weight: 1.00
Evidence: 0.21
Plausible(number, be closed under multiplication)
Evidence: 0.11
¬ Typical(rational number, be closed under multiplication)
0.47
Rule weight: 0.66
Evidence weight: 0.93
Similarity weight: 0.76
Evidence: 0.37
Evidence: 0.11
¬ Typical(rational number, be closed under multiplication)
0.45
Rule weight: 0.66
Evidence weight: 0.89
Similarity weight: 0.76
Evidence: 0.01
Plausible(real number, be closed under addition)
Evidence: 0.11
¬ Typical(rational number, be closed under multiplication)

### Plausibility inheritance from parent to child

0.08
Rule weight: 0.09
Evidence weight: 0.82
Similarity weight: 1.00
Evidence: 0.14
Plausible(rational number, be closed under multiplication)
Evidence: 0.21
¬ Plausible(number, be closed under multiplication)
0.07
Rule weight: 0.09
Evidence weight: 0.99
Similarity weight: 0.76
Evidence: 0.14
Plausible(rational number, be closed under multiplication)
Evidence: 0.01
¬ Plausible(real number, be closed under addition)
0.05
Rule weight: 0.09
Evidence weight: 0.68
Similarity weight: 0.76
Evidence: 0.14
Plausible(rational number, be closed under multiplication)
Evidence: 0.37
¬ Plausible(number, be closed under addition)

### Remarkability exclusitivity betweem a parent and a child

0.58
Rule weight: 0.58
Evidence weight: 1.00
Similarity weight: 1.00
Evidence: 0.00
¬ Remarkable(rational number, be closed under multiplication)
Evidence: 0.19
¬ Remarkable(number, be closed under multiplication)
0.44
Rule weight: 0.58
Evidence weight: 1.00
Similarity weight: 0.76
Evidence: 0.00
¬ Remarkable(rational number, be closed under multiplication)
Evidence: 0.01
¬ Remarkable(real number, be closed under addition)
0.44
Rule weight: 0.58
Evidence weight: 1.00
Similarity weight: 0.76
Evidence: 0.00
¬ Remarkable(rational number, be closed under multiplication)
Evidence: 0.26
¬ Remarkable(number, be closed under addition)

### Remarkability exclusitivity between siblings

0.13
Rule weight: 0.13
Evidence weight: 1.00
Similarity weight: 1.00
Evidence: 0.00
¬ Remarkable(rational number, be closed under multiplication)
Evidence: 0.09
¬ Remarkable(integer, be closed under multiplication)
0.11
Rule weight: 0.13
Evidence weight: 1.00
Similarity weight: 0.81
Evidence: 0.00
¬ Remarkable(rational number, be closed under multiplication)
Evidence: 0.06
¬ Remarkable(integer, be closed under subtraction)
0.10
Rule weight: 0.13
Evidence weight: 1.00
Similarity weight: 0.76
Evidence: 0.00
¬ Remarkable(rational number, be closed under multiplication)
Evidence: 0.15
¬ Remarkable(integer, be closed under addition)

### Remarkability from parent implausibility

0.37
Rule weight: 0.42
Evidence weight: 0.89
Similarity weight: 1.00
Evidence: 0.21
Plausible(number, be closed under multiplication)
Evidence: 0.00
Remarkable(rational number, be closed under multiplication)
Evidence: 0.14
¬ Plausible(rational number, be closed under multiplication)
0.29
Rule weight: 0.42
Evidence weight: 0.91
Similarity weight: 0.76
Evidence: 0.37
Evidence: 0.00
Remarkable(rational number, be closed under multiplication)
Evidence: 0.14
¬ Plausible(rational number, be closed under multiplication)
0.27
Rule weight: 0.42
Evidence weight: 0.86
Similarity weight: 0.76
Evidence: 0.01
Plausible(real number, be closed under addition)
Evidence: 0.00
Remarkable(rational number, be closed under multiplication)
Evidence: 0.14
¬ Plausible(rational number, be closed under multiplication)

### Remarkability from sibling implausibility

0.57
Rule weight: 0.60
Evidence weight: 0.94
Similarity weight: 1.00
Evidence: 0.14
Plausible(rational number, be closed under multiplication)
Evidence: 0.09
Remarkable(integer, be closed under multiplication)
Evidence: 0.07
¬ Plausible(integer, be closed under multiplication)
0.32
Rule weight: 0.60
Evidence weight: 0.65
Similarity weight: 0.81
Evidence: 0.14
Plausible(rational number, be closed under multiplication)
Evidence: 0.06
Remarkable(integer, be closed under subtraction)
Evidence: 0.43
¬ Plausible(integer, be closed under subtraction)
0.20
Rule weight: 0.60
Evidence weight: 0.44
Similarity weight: 0.76
Evidence: 0.14
Plausible(rational number, be closed under multiplication)
Evidence: 0.15
Evidence: 0.76
¬ Plausible(integer, be closed under addition)

### Salient implies Plausible

0.28
Rule weight: 0.28
Evidence weight: 1.00
Similarity weight: 1.00
Evidence: 0.14
Plausible(rational number, be closed under multiplication)
Evidence: 0.00
¬ Salient(rational number, be closed under multiplication)

### Similarity expansion

0.69
Rule weight: 0.85
Evidence weight: 1.00
Similarity weight: 0.81
Evidence: 0.00
Remarkable(rational number, be closed under multiplication)
Evidence: 0.00
¬ Remarkable(rational number, be closed under subtraction)
0.69
Rule weight: 0.85
Evidence weight: 1.00
Similarity weight: 0.81
Evidence: 0.00
Salient(rational number, be closed under multiplication)
Evidence: 0.00
¬ Salient(rational number, be closed under subtraction)
0.66
Rule weight: 0.85
Evidence weight: 1.00
Similarity weight: 0.77
Evidence: 0.00
Salient(rational number, be closed under multiplication)
Evidence: 0.00
¬ Salient(rational number, be closed under division)
0.65
Rule weight: 0.85
Evidence weight: 1.00
Similarity weight: 0.77
Evidence: 0.14
Plausible(rational number, be closed under multiplication)
Evidence: 0.00
¬ Plausible(rational number, be closed under division)
0.65
Rule weight: 0.85
Evidence weight: 1.00
Similarity weight: 0.77
Evidence: 0.00
Remarkable(rational number, be closed under multiplication)
Evidence: 0.00
¬ Remarkable(rational number, be closed under division)
0.65
Rule weight: 0.85
Evidence weight: 1.00
Similarity weight: 0.76
Evidence: 0.00
Remarkable(rational number, be closed under multiplication)
Evidence: 0.00
¬ Remarkable(rational number, be closed in subtraction)
0.65
Rule weight: 0.85
Evidence weight: 1.00
Similarity weight: 0.76
Evidence: 0.00
Salient(rational number, be closed under multiplication)
Evidence: 0.00
¬ Salient(rational number, be closed in subtraction)
0.64
Rule weight: 0.85
Evidence weight: 1.00
Similarity weight: 0.76
Evidence: 0.00
Salient(rational number, be closed under multiplication)
Evidence: 0.00
¬ Salient(rational number, be closed under addition)
0.64
Rule weight: 0.85
Evidence weight: 1.00
Similarity weight: 0.76
Evidence: 0.14
Plausible(rational number, be closed under multiplication)
Evidence: 0.00
¬ Plausible(rational number, be closed under addition)
0.64
Rule weight: 0.85
Evidence weight: 1.00
Similarity weight: 0.76
Evidence: 0.00
Remarkable(rational number, be closed under multiplication)
Evidence: 0.00
¬ Remarkable(rational number, be closed under addition)
0.62
Rule weight: 0.85
Evidence weight: 0.91
Similarity weight: 0.81
Evidence: 0.11
Typical(rational number, be closed under multiplication)
Evidence: 0.11
¬ Typical(rational number, be closed under subtraction)
0.61
Rule weight: 0.85
Evidence weight: 0.88
Similarity weight: 0.81
Evidence: 0.14
Plausible(rational number, be closed under multiplication)
Evidence: 0.14
¬ Plausible(rational number, be closed under subtraction)
0.60
Rule weight: 0.85
Evidence weight: 0.91
Similarity weight: 0.77
Evidence: 0.11
Typical(rational number, be closed under multiplication)
Evidence: 0.10
¬ Typical(rational number, be closed under division)
0.59
Rule weight: 0.85
Evidence weight: 0.91
Similarity weight: 0.76
Evidence: 0.11
Typical(rational number, be closed under multiplication)
Evidence: 0.11
¬ Typical(rational number, be closed in subtraction)
0.58
Rule weight: 0.85
Evidence weight: 0.90
Similarity weight: 0.76
Evidence: 0.11
Typical(rational number, be closed under multiplication)
Evidence: 0.11
¬ Typical(rational number, be closed under addition)
0.57
Rule weight: 0.85
Evidence weight: 0.88
Similarity weight: 0.76
Evidence: 0.14
Plausible(rational number, be closed under multiplication)
Evidence: 0.14
¬ Plausible(rational number, be closed in subtraction)

### Typical and Remarkable implies Salient

0.14
Rule weight: 0.14
Evidence weight: 1.00
Similarity weight: 1.00
Evidence: 0.00
Salient(rational number, be closed under multiplication)
Evidence: 0.11
¬ Typical(rational number, be closed under multiplication)
Evidence: 0.00
¬ Remarkable(rational number, be closed under multiplication)

### Typical implies Plausible

0.43
Rule weight: 0.48
Evidence weight: 0.91
Similarity weight: 1.00
Evidence: 0.14
Plausible(rational number, be closed under multiplication)
Evidence: 0.11
¬ Typical(rational number, be closed under multiplication)

### Typicality and Rermarkability incompatibility between a parent and a child

0.51
Rule weight: 0.51
Evidence weight: 1.00
Similarity weight: 1.00
Evidence: 0.00
¬ Remarkable(rational number, be closed under multiplication)
Evidence: 0.49
¬ Typical(number, be closed under multiplication)
0.39
Rule weight: 0.51
Evidence weight: 1.00
Similarity weight: 0.76
Evidence: 0.00
¬ Remarkable(rational number, be closed under multiplication)
Evidence: 0.14
¬ Typical(real number, be closed under addition)
0.39
Rule weight: 0.51
Evidence weight: 1.00
Similarity weight: 0.76
Evidence: 0.00
¬ Remarkable(rational number, be closed under multiplication)
Evidence: 0.61
¬ Typical(number, be closed under addition)

### Typicality and Rermarkability incompatibility between siblings

0.14
Rule weight: 0.14
Evidence weight: 1.00
Similarity weight: 1.00
Evidence: 0.00
¬ Remarkable(rational number, be closed under multiplication)
Evidence: 0.27
¬ Typical(integer, be closed under multiplication)
0.11
Rule weight: 0.14
Evidence weight: 1.00
Similarity weight: 0.81
Evidence: 0.00
¬ Remarkable(rational number, be closed under multiplication)
Evidence: 0.31
¬ Typical(integer, be closed under subtraction)
0.10
Rule weight: 0.14
Evidence weight: 1.00
Similarity weight: 0.76
Evidence: 0.00
¬ Remarkable(rational number, be closed under multiplication)
Evidence: 0.58
¬ Typical(integer, be closed under addition)

### Typicality inheritance from parent to child

0.32
Rule weight: 0.48
Evidence weight: 0.88
Similarity weight: 0.76
Evidence: 0.11
Typical(rational number, be closed under multiplication)
Evidence: 0.14
¬ Typical(real number, be closed under addition)
0.27
Rule weight: 0.48
Evidence weight: 0.56
Similarity weight: 1.00
Evidence: 0.11
Typical(rational number, be closed under multiplication)
Evidence: 0.49
¬ Typical(number, be closed under multiplication)
0.17
Rule weight: 0.48
Evidence weight: 0.45
Similarity weight: 0.76
Evidence: 0.11
Typical(rational number, be closed under multiplication)
Evidence: 0.61
¬ Typical(number, be closed under addition)