deduction as a service

Mohamed BassemJuly 28, 2015

German University in Cairo

table of contents

1. What is E?

2. Large Axiom Sets

3. Problem

4. Deduction Server

5. Results

6. Future Work

7. Conclusion

2

what is e?

what is e?

E is a theorem prover that takes a set of axioms and tries to derive aformal proof to a given conjuncture

Example:

4

what is e?

E is a theorem prover that takes a set of axioms and tries to derive aformal proof to a given conjunctureExample:

4

large axiom sets

large axiom sets

• OpenCYC library tries to collect the human’s common senseknowledge into a comprehensive library with the aim of allowingAI applications to perfom human-like reasoning[1]

• Up to 500MB of data and millions of axioms• Other huge axiom sets are extracted from libraries such asSUMO and MIZAR

6

large axiom sets

• OpenCYC library tries to collect the human’s common senseknowledge into a comprehensive library with the aim of allowingAI applications to perfom human-like reasoning[1]

• Up to 500MB of data and millions of axioms

• Other huge axiom sets are extracted from libraries such asSUMO and MIZAR

6

large axiom sets

• OpenCYC library tries to collect the human’s common senseknowledge into a comprehensive library with the aim of allowingAI applications to perfom human-like reasoning[1]

• Up to 500MB of data and millions of axioms• Other huge axiom sets are extracted from libraries such asSUMO and MIZAR

6

problem

problem

Usually queries only reRunning multiple queries against the sameknowledge base requires re-parsing the whole set

8

problem

No formal way of communicating with E

9

deduction server

revisiting the problem

11

deduction server: sessions

12

deduction server: server client architecture

13

deduction server: pruning

14

deduction server: parallelization

15

deduction server: interaction protocol

16

deduction server

Live Demo!

17

results

benchmarking

• Tests were performed on a virtualized server with 4 2.6 GHz IntelCPUs with 8 threads

• Chosen TPTP Problems:

• 51 Problems• 479 Megabytes on disk• 3,341,984 Formulae

• Test Setup:

• The deduction server ran in the single strategy mode using thesame strategy as the plain eprover

• Time Limit: 30 Seconds• Memory Limit: 1024 MB

• Time was recorded after 5, 10, 20, 30, 40 and all 51 problems

19

benchmarking

• Tests were performed on a virtualized server with 4 2.6 GHz IntelCPUs with 8 threads

• Chosen TPTP Problems:

• 51 Problems• 479 Megabytes on disk• 3,341,984 Formulae

• Test Setup:

• The deduction server ran in the single strategy mode using thesame strategy as the plain eprover

• Time Limit: 30 Seconds• Memory Limit: 1024 MB

• Time was recorded after 5, 10, 20, 30, 40 and all 51 problems

19

benchmarking

• Tests were performed on a virtualized server with 4 2.6 GHz IntelCPUs with 8 threads

• Chosen TPTP Problems:• 51 Problems

• 479 Megabytes on disk• 3,341,984 Formulae

• Test Setup:

• The deduction server ran in the single strategy mode using thesame strategy as the plain eprover

• Time Limit: 30 Seconds• Memory Limit: 1024 MB

• Time was recorded after 5, 10, 20, 30, 40 and all 51 problems

19

benchmarking

• Tests were performed on a virtualized server with 4 2.6 GHz IntelCPUs with 8 threads

• Chosen TPTP Problems:• 51 Problems• 479 Megabytes on disk

• 3,341,984 Formulae

• Test Setup:

• The deduction server ran in the single strategy mode using thesame strategy as the plain eprover

• Time Limit: 30 Seconds• Memory Limit: 1024 MB

• Time was recorded after 5, 10, 20, 30, 40 and all 51 problems

19

benchmarking

• Tests were performed on a virtualized server with 4 2.6 GHz IntelCPUs with 8 threads

• Chosen TPTP Problems:• 51 Problems• 479 Megabytes on disk• 3,341,984 Formulae

• Test Setup:

• The deduction server ran in the single strategy mode using thesame strategy as the plain eprover

• Time Limit: 30 Seconds• Memory Limit: 1024 MB

• Time was recorded after 5, 10, 20, 30, 40 and all 51 problems

19

benchmarking

• Tests were performed on a virtualized server with 4 2.6 GHz IntelCPUs with 8 threads

• Chosen TPTP Problems:• 51 Problems• 479 Megabytes on disk• 3,341,984 Formulae

• Test Setup:

• The deduction server ran in the single strategy mode using thesame strategy as the plain eprover

• Time Limit: 30 Seconds• Memory Limit: 1024 MB

• Time was recorded after 5, 10, 20, 30, 40 and all 51 problems

19

benchmarking

• Tests were performed on a virtualized server with 4 2.6 GHz IntelCPUs with 8 threads

• Chosen TPTP Problems:• 51 Problems• 479 Megabytes on disk• 3,341,984 Formulae

• Test Setup:• The deduction server ran in the single strategy mode using thesame strategy as the plain eprover

• Time Limit: 30 Seconds• Memory Limit: 1024 MB

• Time was recorded after 5, 10, 20, 30, 40 and all 51 problems

19

benchmarking

• Tests were performed on a virtualized server with 4 2.6 GHz IntelCPUs with 8 threads

• Chosen TPTP Problems:• 51 Problems• 479 Megabytes on disk• 3,341,984 Formulae

• Test Setup:• The deduction server ran in the single strategy mode using thesame strategy as the plain eprover

• Time Limit: 30 Seconds

• Memory Limit: 1024 MB

• Time was recorded after 5, 10, 20, 30, 40 and all 51 problems

19

benchmarking

• Tests were performed on a virtualized server with 4 2.6 GHz IntelCPUs with 8 threads

• Chosen TPTP Problems:• 51 Problems• 479 Megabytes on disk• 3,341,984 Formulae

• Test Setup:• The deduction server ran in the single strategy mode using thesame strategy as the plain eprover

• Time Limit: 30 Seconds• Memory Limit: 1024 MB

• Time was recorded after 5, 10, 20, 30, 40 and all 51 problems

19

benchmarking

• Tests were performed on a virtualized server with 4 2.6 GHz IntelCPUs with 8 threads

• Chosen TPTP Problems:• 51 Problems• 479 Megabytes on disk• 3,341,984 Formulae

• Test Setup:• The deduction server ran in the single strategy mode using thesame strategy as the plain eprover

• Time Limit: 30 Seconds• Memory Limit: 1024 MB

• Time was recorded after 5, 10, 20, 30, 40 and all 51 problems

19

benchmarking

20

deduction as a service

• Having a hosted deduction server will allow users to connect tothe remote server and have their own sessions

• A win for:

• Users who cannot install the prover due to compatiblity issues• Users who have limited resources

• Before The protocol, apps used to interacting with E by invokingthe executable in a subprocess. The interaction protocl willmake it much easier to intgerate apps with E

21

deduction as a service

• Having a hosted deduction server will allow users to connect tothe remote server and have their own sessions

• A win for:

• Users who cannot install the prover due to compatiblity issues• Users who have limited resources

• Before The protocol, apps used to interacting with E by invokingthe executable in a subprocess. The interaction protocl willmake it much easier to intgerate apps with E

21

deduction as a service

• Having a hosted deduction server will allow users to connect tothe remote server and have their own sessions

• A win for:• Users who cannot install the prover due to compatiblity issues

• Users who have limited resources

• Before The protocol, apps used to interacting with E by invokingthe executable in a subprocess. The interaction protocl willmake it much easier to intgerate apps with E

21

deduction as a service

• Having a hosted deduction server will allow users to connect tothe remote server and have their own sessions

• A win for:• Users who cannot install the prover due to compatiblity issues• Users who have limited resources

• Before The protocol, apps used to interacting with E by invokingthe executable in a subprocess. The interaction protocl willmake it much easier to intgerate apps with E

21

deduction as a service

• Having a hosted deduction server will allow users to connect tothe remote server and have their own sessions

• A win for:• Users who cannot install the prover due to compatiblity issues• Users who have limited resources

• Before The protocol, apps used to interacting with E by invokingthe executable in a subprocess. The interaction protocl willmake it much easier to intgerate apps with E

21

future work

future work

• Controlling client allowed resource

• Clustering and load balancing• Supporting other backends• Supporting other pruning techniques

23

future work

• Controlling client allowed resource• Clustering and load balancing

• Supporting other backends• Supporting other pruning techniques

23

future work

• Controlling client allowed resource• Clustering and load balancing• Supporting other backends

• Supporting other pruning techniques

23

future work

• Controlling client allowed resource• Clustering and load balancing• Supporting other backends• Supporting other pruning techniques

23

conclusion

• Benchmarking results shows that the deduction server modeoutperforms plain eprover in large axiom sets with sharedknowledge bases

• Offering deduction as a hosted service will allow users to useremote theorem provers on powerful servers

• The interaction protocol makes integrating apps with E mucheasier

25

• Benchmarking results shows that the deduction server modeoutperforms plain eprover in large axiom sets with sharedknowledge bases

• Offering deduction as a hosted service will allow users to useremote theorem provers on powerful servers

• The interaction protocol makes integrating apps with E mucheasier

25

• Benchmarking results shows that the deduction server modeoutperforms plain eprover in large axiom sets with sharedknowledge bases

• Offering deduction as a hosted service will allow users to useremote theorem provers on powerful servers

• The interaction protocol makes integrating apps with E mucheasier

25

Questions?

26

Thank you

27

references I

Opencyc — Wikipedia, the free encyclopedia.[Online; accessed 28-July-2015].

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