The Reasoning and Optimization Theme Joshua Knowles, Konstantin Korovin and Renate Schmidt School of Computer Science The University of Manchester September 16, 2014 J. Knowles, K. Korovin & R. Schmidt (Computer Science) Reasoning and Optimization Theme September 16, 2014 1 / 22
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The Reasoning and Optimization Theme
Joshua Knowles, Konstantin Korovin and Renate Schmidt
School of Computer ScienceThe University of Manchester
September 16, 2014
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 1 / 22
Outline
1 Why Automated Reasoning?
2 Why Optimization?
3 General practical remarks
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 2 / 22
Automated Reasoning
What is Reasoning? Solving problems by syntactic manipulations.
Hardware: Are these two hardware designs equivalent?
Software: Does your program accesses unallocated memory?
Math: Does this equation (xy)−1 = y−1x−1 hold in all groups?
Knowledge management:Can we represent and analyse all available knowledge about human body ?
Automated reasoning: can we solve all these problems automatically ?
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 3 / 22
Automated Reasoning
What is Reasoning? Solving problems by syntactic manipulations.
Hardware: Are these two hardware designs equivalent?
Software: Does your program accesses unallocated memory?
Math: Does this equation (xy)−1 = y−1x−1 hold in all groups?
Knowledge management:Can we represent and analyse all available knowledge about human body ?
Automated reasoning: can we solve all these problems automatically ?
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 3 / 22
Automated Reasoning
What is Reasoning? Solving problems by syntactic manipulations.
Hardware: Are these two hardware designs equivalent?
Software: Does your program accesses unallocated memory?
Math: Does this equation (xy)−1 = y−1x−1 hold in all groups?
Knowledge management:Can we represent and analyse all available knowledge about human body ?
Automated reasoning: can we solve all these problems automatically ?
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 3 / 22
Automated Reasoning
What is Reasoning? Solving problems by syntactic manipulations.
Hardware: Are these two hardware designs equivalent?
Software: Does your program accesses unallocated memory?
Math: Does this equation (xy)−1 = y−1x−1 hold in all groups?
Knowledge management:Can we represent and analyse all available knowledge about human body ?
Automated reasoning: can we solve all these problems automatically ?
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 3 / 22
Automated Reasoning
What is Reasoning? Solving problems by syntactic manipulations.
Hardware: Are these two hardware designs equivalent?
Software: Does your program accesses unallocated memory?
Math: Does this equation (xy)−1 = y−1x−1 hold in all groups?
Knowledge management:Can we represent and analyse all available knowledge about human body ?
Automated reasoning: can we solve all these problems automatically ?
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 3 / 22
Automated Reasoning
What is Reasoning? Solving problems by syntactic manipulations.
Hardware: Are these two hardware designs equivalent?
Software: Does your program accesses unallocated memory?
Math: Does this equation (xy)−1 = y−1x−1 hold in all groups?
Knowledge management:Can we represent and analyse all available knowledge about human body ?
Automated reasoning: can we solve all these problems automatically ?
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 3 / 22
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 4 / 22
Manchester: world leading in logic and reasoning
Theory:
first-order reasoningresolution, superposition, instantiation, tableaux, linear arithmeticontology reasoning
Applications:
software/hardware verificationsemantic Web, bio-healthmulti-agent systems
Reasoning systems developed in our School:iProver – an instantiation-based reasoner for first-orderlogic won major of awards at CASC championships.Vampire – a superposition-based reasoner for first-orderlogic, won major awards at CASC championships.MSPASS – a resolution/superposition based reasoner SPASS extendedwith reasoning with modal logics.Fact++ an ontology reasoner: OWL DL.Pellet an ontology reasoner: OWL DL.
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 5 / 22
Manchester: world leading in logic and reasoning
Theory:
first-order reasoningresolution, superposition, instantiation, tableaux, linear arithmeticontology reasoning
Applications:
software/hardware verificationsemantic Web, bio-healthmulti-agent systems
Reasoning systems developed in our School:iProver – an instantiation-based reasoner for first-orderlogic won major of awards at CASC championships.Vampire – a superposition-based reasoner for first-orderlogic, won major awards at CASC championships.MSPASS – a resolution/superposition based reasoner SPASS extendedwith reasoning with modal logics.Fact++ an ontology reasoner: OWL DL.Pellet an ontology reasoner: OWL DL.
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 5 / 22
Manchester: world leading in logic and reasoning
Theory:
first-order reasoningresolution, superposition, instantiation, tableaux, linear arithmeticontology reasoning
Applications:
software/hardware verificationsemantic Web, bio-healthmulti-agent systems
Reasoning systems developed in our School:iProver – an instantiation-based reasoner for first-orderlogic won major of awards at CASC championships.Vampire – a superposition-based reasoner for first-orderlogic, won major awards at CASC championships.MSPASS – a resolution/superposition based reasoner SPASS extendedwith reasoning with modal logics.Fact++ an ontology reasoner: OWL DL.Pellet an ontology reasoner: OWL DL.
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 5 / 22
COMP60332 – Automated Reasoning and Verification
This course is focused on efficient automated reasoning.This course is self-contained but assumes that students are comfortablewith mathematical notions.
First-order logic: syntax, semantics, SkolemizationFirst-order resolutionHow to prove all mathematical theorems using only two rules?Elegant mathematical framework for completenessModel construction, well-founded inductionHow to make reasoning efficient: redundancy eliminationWhat is inside a theorem prover ?
Applications: verification
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 6 / 22
COMP60332 – Automated Reasoning and Verification
This course is focused on efficient automated reasoning.This course is self-contained but assumes that students are comfortablewith mathematical notions.
First-order logic: syntax, semantics, SkolemizationFirst-order resolutionHow to prove all mathematical theorems using only two rules?Elegant mathematical framework for completenessModel construction, well-founded inductionHow to make reasoning efficient: redundancy eliminationWhat is inside a theorem prover ?
Applications: verification
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 6 / 22
COMP60332 – Automated Reasoning and Verification
This course is focused on efficient automated reasoning.This course is self-contained but assumes that students are comfortablewith mathematical notions.
First-order logic: syntax, semantics, SkolemizationFirst-order resolutionHow to prove all mathematical theorems using only two rules?Elegant mathematical framework for completenessModel construction, well-founded inductionHow to make reasoning efficient: redundancy eliminationWhat is inside a theorem prover ?
Applications: verification
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 6 / 22
COMP60332 – Automated Reasoning and Verification
This course is focused on efficient automated reasoning.This course is self-contained but assumes that students are comfortablewith mathematical notions.
First-order logic: syntax, semantics, SkolemizationFirst-order resolutionHow to prove all mathematical theorems using only two rules?Elegant mathematical framework for completenessModel construction, well-founded inductionHow to make reasoning efficient: redundancy eliminationWhat is inside a theorem prover ?
Applications: verification
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 6 / 22
COMP60332 – Automated Reasoning and Verification
This course is focused on efficient automated reasoning.This course is self-contained but assumes that students are comfortablewith mathematical notions.
First-order logic: syntax, semantics, SkolemizationFirst-order resolutionHow to prove all mathematical theorems using only two rules?Elegant mathematical framework for completenessModel construction, well-founded inductionHow to make reasoning efficient: redundancy eliminationWhat is inside a theorem prover ?
Applications: verification
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 6 / 22
Assessment
Exam: 50%Closed book, 2 hours, choose 3 out of 4 questions
Coursework and lab: 50%Assessed and unassessed exercises: pen and paperLabwork involving
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 7 / 22
Why Optimization?
...we recognize efficiency, strength, compactness in these designs. Howcan we mechanize the design process?
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 8 / 22
Why Optimization?
It means finding the best; a fundamental aim in all human endeavour
Optimization saves and makes money; underpins engineering; helpsorganize, manage and plan; supports machine learning; solvesproblems
Computers can do it fast
It is deeply linked with Reasoning by the structure of problems
It is philosophically linked with mathematics, intelligence,computation, e.g., through the theory of NP-completeness
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 9 / 22
Optimization in Machine Learning
Hamiltonian
of a double pendulum discovered by
computer
Computer Derives Physical Laws by ItelfIn 2009, Cornell researchers, Schmidt andLipson, used an optimization method based onadvanced symbolic regression to “discover”physical laws automatically from motion data.(Science, 2009)
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 10 / 22
Optimization in Machine Learning
Researchers at Manchester in 2011, developed optimization techniquesto discover combination therapies to treat brain inflammation, a majorfactor in Alzheimer’s and other diseases. (Nature Chemical Biology, 2011)
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 11 / 22
Optimization in Planning
The Hubble Space Telescope is a scarceresource.
Advanced optimization algorithms are used toschedule time on the telescope, sharing theresource between different groups and takingaccount of constraints
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 12 / 22
Optimization Saves Money
IcoSystem (a US optimization andcomplexity science company) set outto improve drug developmentprocesses at Eli Lilly.
‘Compared to a standard 40 months androughly £25 million, ...[we] reached thesame amount of technical success in a yearand a day with a total expenditure on theorder of £2.7 million.’ –Neil Bodick, COO,Eli Lilly Chorus
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 13 / 22
Optimization in Problem Solving
What is the minimum number ofmoves (from here) to obtain asolved cube?
What about from ANYconfiguration?
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 14 / 22
COMP60342 – What You Will Learn
The course aims to have a practical outcome
You will learn
How to approach a wide variety of problems, and how to developyour own code to solve them
You will understand some of the most general and flexible optimizationalgorithms, and how and why they work
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 15 / 22
What You Will Learn 2
Some important and interesting mathematical theory behind the practice
This links optimization fundamentally to computation and the notion ofcomplexity
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 16 / 22
How You Will Learn It
Answering thought-provoking questions (often not assessed)
Doing LAB work, where YOU MUST CODE for yourself
Running experiments in LABs where you test and compare methods
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 17 / 22
Structure of the Course
Week 1: Introduction to OptimizationProblems: from MAX-SAT to TSP to Optimal BettingBasic exact methods: Enumeration and Greedy
Up-to-date detailsSee timetable and course unit descriptions on the webSee also separate webpages for individual course units: containadditional material such as slides, links to tools, etc
J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme September 16, 2014 22 / 22