Jasper De Bock & Gert de Cooman
ISIPTA 2019
coherent choice functions
in terms of desirability Interpreting, axiomatising and representing
coherent choice functions in terms of desirability Jasper De Bock - - PowerPoint PPT Presentation
Interpreting, axiomatising and representing coherent choice functions in terms of desirability Jasper De Bock & Gert de Cooman ISIPTA 2019 Interpreting, axiomatising and representing coherent choice functions ? in terms of desirability
Jasper De Bock & Gert de Cooman
ISIPTA 2019
in terms of desirability Interpreting, axiomatising and representing
in terms of desirability Interpreting, axiomatising and representing
in terms of desirability Interpreting, axiomatising and representing
in terms of desirability Interpreting, axiomatising and representing
in terms of desirability Interpreting, axiomatising and representing
in terms of desirability Interpreting, axiomatising and representing
in terms of desirability Interpreting, axiomatising and representing
v1
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v1
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∈
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desirable option
elementary concept
∈ V
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<latexit sha1_base64="iwmWt1RWEC35dw0fLmLkGU9fsw4=">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</latexit><latexit sha1_base64="prEBMFT6cFmVviTsasrMSzQLwE=">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</latexit><latexit sha1_base64="prEBMFT6cFmVviTsasrMSzQLwE=">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</latexit><latexit sha1_base64="pyTVy014yb3dNI3WGibcaSh/g=">ACxHicjVHLSsNAFD2Nr1pfVZdugkVwVRI3uiwK4rIF+4BaJEmndeg0CZlJoRT9Abf6beIf6F94Z5yCWkQnJDlz7j1n5t4bpoJL5XmvBWdpeWV1rbhe2tjc2t4p7+61ZJnEWtGiUiyThIJnjMmorwTpxoJxKFg7HF3oeHvCMsmT+FpNU9YbB8OYD3gUKIak9tyxat6ZrmLwLegArvqSfkFN+gjQYQcYzDEUIQFAkh6uvDhISWuhxlxGSFu4gz3KJE2pyxGQGxI/oOade1bEx7SmNOqJTBL0ZKV0ckSahvIywPs018dw4a/Y375nx1Heb0j+0XmNiFe6I/Us3z/yvTteiMCZqYFTalhdHWRdclNV/TN3S9VKXJIidO4T/GMcGSU8z67RiN7bq3gYm/mUzN6n1kc3O861vSgP2f41wErZOq71X9hl+pndtRF3GAQxzTPE9RwxXqaBrvRzh2bl0hCOd/DPVKVjNPr4t5+EDZWyPeA=</latexit>strictly preferred
in terms of desirability Interpreting, axiomatising and representing
set of desirable options D
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derived notion 1
desirable option
elementary concept
∈ V
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sets of desirable options / partial preference orderings lower and upper expectations/previsions closed convex sets of probability measures lower and upper probabilities belief and plausibility functions possibility and necessity measures probability measures
set of desirable options D
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derived notion 1
sets of desirable options / partial preference orderings lower and upper probabilities belief and plausibility functions possibility and necessity measures probability measures lower and upper expectations/previsions closed convex sets of probability measures
P1
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derived notion 1
sets of desirable options / partial preference orderings lower and upper probabilities belief and plausibility functions possibility and necessity measures probability measures lower and upper expectations/previsions closed convex sets of probability measures
P1
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derived notion 1
in terms of desirability Interpreting, axiomatising and representing
desirable option set
⊆ V
<latexit sha1_base64="Zh/aGiLZzmnenb/eWc8yWRPy3Y=">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</latexit><latexit sha1_base64="ghu38LDudNBxfsr/HzaDx8G8qM=">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</latexit><latexit sha1_base64="ghu38LDudNBxfsr/HzaDx8G8qM=">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</latexit><latexit sha1_base64="OqGYekwi6TEdb3TV0CBnGzOG6WI=">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</latexit>A
<latexit sha1_base64="VEFQrEez+HNYg/4eyC3xP79vYWo=">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</latexit><latexit sha1_base64="rWfatWFD9JywsFetZXGA0z5awm4=">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</latexit><latexit sha1_base64="rWfatWFD9JywsFetZXGA0z5awm4=">ACxHicjVHLSsNAFD2NrxpfVZdugkVwVRI3uhGrgrhswT6gFknSaQ1NkzAzEUrRH3CrX+DH+AnFP9C/8M40BbWITkhy5txzsyd8ZIwENK23LG3PzC4lJ+2VxZXVvfKGxu1UWcp/V/DiMedNzBQuDiNVkIEPWTDhzB17IGl7/XNUbd4yLI6u5DBh7YHbi4Ju4LuSqOrpTaFol2w9rFngZKB48moeJy9jsxIXxrhGBzF8pBiAIYIkHMKFoKcFBzYS4toYEcJBbrOcA+TvCmpGClcYv07dGslbERzVWm0G6fVgnp5eS0sEemHScsFrN0vVUJyv2t+yRzlR7G9Lfy7IGxErcEvuXb6r8r0/1ItHFke4hoJ4Szaju/Cwl1aeidm596UpSQkKcwh2qc8K+dk7P2dIeoXtXZ+vq+rtWKlbN/Uyb4kPtki7Y+Xmds6B+UHLsklN1iuUzTEYeO9jFPt3nIcq4RAU1nf2IJzwbF0ZoCOdSI1c5tnGt2E8fAIUXJKE</latexit><latexit sha1_base64="2TudwOvph/JvSAesHzyZm+2CF8=">ACxHicjVHLSsNAFD2Nr1pfVZdugkVwVRI3uqwK4rIF+4BaJEmndeg0CZmJUIr+gFv9NvEP9C+8M05BLaITkpw5954zc+8NU8Gl8rzXgrOwuLS8Ulwtra1vbG6Vt3daMsmziDWjRCRZJwkEzxmTcWVYJ0Y8E4FKwdjs51vH3HMsmT+EpNUtYbB8OYD3gUKIapzflilf1zHLngW9BXbVk/ILrtFHg5xmCIoQgLBJD0dOHDQ0pcD1PiMkLcxBnuUSJtTlmMgJiR/Qd0q5r2Zj2lMadUSnCHozUro4IE1CeRlhfZpr4rlx1uxv3lPjqe82oX9ovcbEKtwS+5dulvlfna5FYATUwOnmlLD6Ooi65Kbruibu1+qUuSQEqdxn+IZ4cgoZ312jUa2nVvAxN/M5ma1fvI5uZ417ekAfs/xzkPWkdV36v6Db9SO7OjLmIP+zikeR6jhkvU0Tej3jCs3PhCEc6+WeqU7CaXxbzsMH532PQw=</latexit>contains at least
desirable option
elementary concept
∈ V
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<latexit sha1_base64="iwmWt1RWEC35dw0fLmLkGU9fsw4=">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</latexit><latexit sha1_base64="prEBMFT6cFmVviTsasrMSzQLwE=">ACxHicjVHLSsNAFD2NrxpfVZdugkVwVRI3uhGLgrhswT6gFknSaQ2dJiEzKZSiP+BWv8CP8ROKf6B/4Z1pCmoRnZDkzLnJk748U8ENK23LGwuLS8kp+1Vxb39jcKmzv1EWUJj6r+RGPkqbnCsaDkNVkIDlrxglzBx5nDa9/oeqNIUtEIXchSz9sDthUE38F1JVHV4WyjaJVsPax4GSievZqn8cvErESFCW7QfKQZgCEJc7gQ9LTgwEZMXBtj4hJCga4z3Mkb0oqRgqX2D59ezRrZWxIc5UptNunVTi9CTktHJAnIl1CWK1m6XqkxX7W/ZYZ6q9jejvZVkDYiXuiP3LN1P+16d6kejiRPcQUE+xZlR3fpaS6lNRO7e+dCUpISZO4Q7VE8K+ds7O2dIeoXtXZ+vq+rtWKlbN/Uyb4kPtki7Y+Xmd86B+VHLsklN1iuVzTEce9jHId3nMcq4QgU1nf2IJzwblwY3hJFOpUYu8+zi2zAePgGSPJK5</latexit><latexit sha1_base64="prEBMFT6cFmVviTsasrMSzQLwE=">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</latexit><latexit sha1_base64="pyTVy014yb3dNI3WGibcaSh/g=">ACxHicjVHLSsNAFD2Nr1pfVZdugkVwVRI3uiwK4rIF+4BaJEmndeg0CZlJoRT9Abf6beIf6F94Z5yCWkQnJDlz7j1n5t4bpoJL5XmvBWdpeWV1rbhe2tjc2t4p7+61ZJnEWtGiUiyThIJnjMmorwTpxoJxKFg7HF3oeHvCMsmT+FpNU9YbB8OYD3gUKIak9tyxat6ZrmLwLegArvqSfkFN+gjQYQcYzDEUIQFAkh6uvDhISWuhxlxGSFu4gz3KJE2pyxGQGxI/oOade1bEx7SmNOqJTBL0ZKV0ckSahvIywPs018dw4a/Y375nx1Heb0j+0XmNiFe6I/Us3z/yvTteiMCZqYFTalhdHWRdclNV/TN3S9VKXJIidO4T/GMcGSU8z67RiN7bq3gYm/mUzN6n1kc3O861vSgP2f41wErZOq71X9hl+pndtRF3GAQxzTPE9RwxXqaBrvRzh2bl0hCOd/DPVKVjNPr4t5+EDZWyPeA=</latexit>strictly preferred
derived notion 2
in terms of desirability Interpreting, axiomatising and representing
desirable option set
⊆ V
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derived notion 2 derived notion 3
set of desirable
in terms of desirability Interpreting, axiomatising and representing
choice function set of desirable
choice function
sets of desirable options / partial preference orderings lower and upper probabilities belief and plausibility functions possibility and necessity measures probability measures lower and upper expectations/previsions closed convex sets of probability measures
s e t
…
set of desirable
sets of desirable options / partial preference orderings lower and upper probabilities belief and plausibility functions possibility and necessity measures probability measures lower and upper expectations/previsions closed convex sets of probability measures
P1
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…
choice function set of desirable
Interpreting, Axiomatising and Representing Coherent Choice Functions in Terms of Desirability
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