a proof from 1988 that pdl has interpolation
play

A Proof from 1988 that PDL has Interpolation? (1) EDV-Beratung - PowerPoint PPT Presentation

Aug 30, 2023 β€’133 likes β€’502 views

A Proof from 1988 that PDL has Interpolation? (1) EDV-Beratung Manfred Borzechowski, Berlin, Germany (2) University of Groningen, Groningen, The Netherlands Advances in Modal Logic 2020 2020-08-26 15:00 1 Manfred Borzechowski (1) & Malvin

  1. A Proof from 1988 that PDL has Interpolation? (1) EDV-Beratung Manfred Borzechowski, Berlin, Germany (2) University of Groningen, Groningen, The Netherlands Advances in Modal Logic 2020 2020-08-26 15:00 1 Manfred Borzechowski (1) & Malvin Gattinger (2)

  2. Propositional Dynamic Logic (PDL) x: π‘Ÿ β„³, π‘₯ ⊨ ⟨𝐡⟩(βŸ¨π΅βŸ©Β¬π‘Ÿ ∧ ⟨𝐢⟩[𝐢 βˆ— ]π‘Ÿ) β„³, π‘₯ ⊨ [𝐢 βˆ— ]π‘Ÿ β„³, π‘₯ ⊨ [𝐢]π‘Ÿ β„³, π‘₯ ⊨ ⟨𝐡; πΆβŸ©π‘Ÿ B B A A w: π‘Ÿ Syntax v: π‘ž Example Also expressible: β€œif…then…else…” and β€œwhile…do…” ∢∢= 𝑏 π‘ž ∣ ¬𝜚 ∣ 𝜚 ∧ 𝜚 ∣ [𝑏]𝜚 ∢∢= 𝜚 2 𝐡 ∣ 𝑏; 𝑏 ∣ 𝑏 βˆͺ 𝑏 ∣ 𝑏 βˆ— ∣ 𝜚?

  3. Propositional Dynamic Logic (PDL) x: π‘Ÿ β„³, π‘₯ ⊨ ⟨𝐡⟩(βŸ¨π΅βŸ©Β¬π‘Ÿ ∧ ⟨𝐢⟩[𝐢 βˆ— ]π‘Ÿ) β„³, π‘₯ ⊨ [𝐢 βˆ— ]π‘Ÿ β„³, π‘₯ ⊨ [𝐢]π‘Ÿ β„³, π‘₯ ⊨ ⟨𝐡; πΆβŸ©π‘Ÿ B B A A w: π‘Ÿ Syntax v: π‘ž Example Also expressible: β€œif…then…else…” and β€œwhile…do…” ∢∢= 𝑏 π‘ž ∣ ¬𝜚 ∣ 𝜚 ∧ 𝜚 ∣ [𝑏]𝜚 ∢∢= 𝜚 2 𝐡 ∣ 𝑏; 𝑏 ∣ 𝑏 βˆͺ 𝑏 ∣ 𝑏 βˆ— ∣ 𝜚?

  4. Craig Interpolation πœ„ ⟢ (π‘Ÿ ∨ 𝑠) π‘Ÿ (π‘ž ∧ π‘Ÿ) Example (1918 – 2016) William Craig ⟢ πœ” . We then write 𝜚 𝑀(𝜚) ∢= {π‘ž ∣ π‘ž occurs in 𝜚} - 𝑀(πœ„) βŠ† 𝑀(𝜚) ∩ 𝑀(πœ”) πœ„ β†’ πœ” is valid - is valid - 𝜚 β†’ πœ„ A logic has Craig Interpolation iff for any valid Definition 3 𝜚 β†’ πœ” there is an interpolant πœ„ such that:

  5. Logics that (we know) have Craig Interpolation β€’ Propositional Logic β€’ First-Order Logic β€’ Intuitionistic Logic β€’ Basic and Multi-modal logic (MadarΓ‘sz 1995) β€’ 𝜈 -Calculus (D’Agostino and Hollenberg 2000) What about PDL? Language of a formula := all atomic propositions and programs . Example [(𝐡 βˆͺ 𝐢) βˆ— ](π‘ž ∧ π‘Ÿ) [𝐢 βˆ— ]π‘Ÿ ⟢ [(𝐢; 𝐢) βˆ— ](π‘Ÿ ∨ [𝐷]𝑠) Problem: How to find interpolants for βˆ— systematically? 4

  6. Logics that (we know) have Craig Interpolation β€’ Propositional Logic β€’ First-Order Logic β€’ Intuitionistic Logic β€’ Basic and Multi-modal logic (MadarΓ‘sz 1995) β€’ 𝜈 -Calculus (D’Agostino and Hollenberg 2000) What about PDL? Language of a formula := all atomic propositions and programs . Example [(𝐡 βˆͺ 𝐢) βˆ— ](π‘ž ∧ π‘Ÿ) [𝐢 βˆ— ]π‘Ÿ ⟢ [(𝐢; 𝐢) βˆ— ](π‘Ÿ ∨ [𝐷]𝑠) Problem: How to find interpolants for βˆ— systematically? 4

  7. History β€’ Daniel Leivant: Proof theoretic methodology for propositional dynamic logic . Conference paper in LNCS, 1981. β€’ Manfred Borzechowski: Tableau–KalkΓΌl fΓΌr PDL und Interpolation . Diploma thesis, FU Berlin, 1988. β€’ Tomasz Kowalski: PDL has interpolation . Journal of Symbolic Logic, 2002. Revoked in 2004. β€’ Marcus Kracht: Chapter The open question in Tools and Techniques in Modal Logic , 1999. 5

  8. History β€’ Daniel Leivant: Proof theoretic methodology for propositional dynamic logic . Conference paper in LNCS, 1981. β€’ Manfred Borzechowski: Tableau–KalkΓΌl fΓΌr PDL und Interpolation . Diploma thesis, FU Berlin, 1988. β€’ Tomasz Kowalski: PDL has interpolation . Journal of Symbolic Logic, 2002. Revoked in 2004. β€’ Marcus Kracht: Chapter The open question in Tools and Techniques in Modal Logic , 1999. 5

  9. History β€’ Daniel Leivant: Proof theoretic methodology for propositional dynamic logic . Conference paper in LNCS, 1981. β€’ Manfred Borzechowski: Tableau–KalkΓΌl fΓΌr PDL und Interpolation . Diploma thesis, FU Berlin, 1988. β€’ Tomasz Kowalski: PDL has interpolation . Journal of Symbolic Logic, 2002. Revoked in 2004. β€’ Marcus Kracht: Chapter The open question in Tools and Techniques in Modal Logic , 1999. 5

  10. Borzechowski 1988: Why look at it now? β€’ It seems it was never really published. β€’ We now make an English translation available. β€’ Kracht (1999): not β€œpossible to verify the argument” 6

  11. Outline of the proof attempt 1. Define a tableaux system. 2. Show soundness and completeness. 3. Define interpolants for each node β€œbottom-up”. Problems caused by βˆ— : β€’ How to ensure finite tableaux? β€’ How to define interpolants for βˆ— steps? 7

  12. Tableaux Rules: Part 1/2 (Β¬?) π‘Œ; 𝑄; [𝑏][𝑏 (π‘œ) ]𝑄 (π‘œ) π‘Œ; [𝑏 βˆ— ]𝑄 ∣ π‘Œ; Β¬[𝑏][𝑏 (π‘œ) ]𝑄 π‘Œ; ¬𝑄 (Β¬π‘œ) π‘Œ; Β¬[𝑏 βˆ— ]𝑄 π‘Œ; [𝑏; 𝑐]𝑄 π‘Œ; [𝑅?]𝑄 π‘Œ; [𝑏 βˆͺ 𝑐]𝑄 π‘Œ; Β¬[𝑏; 𝑐]𝑄 classical rules: π‘Œ; 𝑅; ¬𝑄 π‘Œ; Β¬[𝑅?]𝑄 π‘Œ; Β¬(𝑄 ∧ 𝑅) π‘Œ; ¬¬𝑄 (Β¬) π‘Œ; 𝑄 π‘Œ; 𝑄 ∧ 𝑅 ( ∧ ) π‘Œ; 𝑄; 𝑅 8 ∣ π‘Œ; Β¬[𝑐]𝑄 ∣ π‘Œ; ¬𝑅 local rules: π‘Œ; Β¬[𝑏 βˆͺ 𝑐]𝑄 (¬∧) π‘Œ; ¬𝑄 (Β¬βˆͺ) π‘Œ; Β¬[𝑏]𝑄 (Β¬; ) π‘Œ; Β¬[𝑏][𝑐]𝑄 (βˆͺ) π‘Œ; [𝑏]𝑄; [𝑐]𝑄 (?) 𝑦; ¬𝑅 ∣ π‘Œ; 𝑄 (; ) π‘Œ; [𝑏][𝑐]𝑄

  13. Tableaux Rules: Part 2/2 (𝐡𝑒) where (…) (Β¬?) (Β¬π‘œ) (Β¬; ) (Β¬βˆͺ) PDL rules: marked rules: the critical rule. 9 π‘Œ free π‘Œ; Β¬[𝑏]𝑄 (π‘βˆ’) the loading rule , π‘Œ; Β¬[𝑏 0 ] … [𝑏 π‘œ ]𝑄 (𝑁+) the liberation rule , π‘Œ; Β¬[𝑏 0 ] … [𝑏 π‘œ ]𝑄 𝑄 π‘Œ; Β¬[𝑏]𝑄 𝑆 π‘Œ; Β¬[𝐡]𝑄 𝑆 π‘Œ 𝐡 ; ¬𝑄 𝑆\𝑄 π‘Œ; Β¬[𝑏 βˆͺ 𝑐]𝑄 𝑆 π‘Œ; Β¬[𝑏; 𝑐]𝑄 𝑆 π‘Œ; Β¬[𝑏]𝑄 𝑆 ∣ π‘Œ; Β¬[𝑐]𝑄 𝑆 π‘Œ; Β¬[𝑏][𝑐]𝑄 𝑆 π‘Œ; Β¬[𝑏 βˆ— ]𝑄 𝑆 π‘Œ; Β¬[𝑅?]𝑄 𝑆 π‘Œ; ¬𝑄 𝑆\𝑄 ∣ π‘Œ; Β¬[𝑏][𝑏 (π‘œ) ]𝑄 𝑆 π‘Œ; 𝑅; ¬𝑄 𝑆\𝑄 𝑆\𝑄 indicates that 𝑆 is removed iff 𝑆 = 𝑄 .

  14. Tableaux Rules: Extra Conditions 1. On reaching π‘Œ; Β¬[𝐡]𝑄 or π‘Œ; [𝐡]𝑄 , change (π‘œ) back to βˆ— in 𝑄 . 2. Instead of π‘Œ; [𝑏 (π‘œ) ]𝑄 we always obtain π‘Œ . 3. A rule must be applied to an π‘œ -formula whenever it is possible. 4. No rule may be applied to a Β¬[𝑏 (π‘œ) ] -node. 5. To a node obtained using (𝑁+) we may not apply (π‘βˆ’) . 6. If a normal node 𝑒 has a predecessor 𝑑 with the same formulas and the path 𝑑 … 𝑒 uses (𝐡𝑒) and is loaded if 𝑑 is loaded, then 𝑒 is an end node. 7. Every loaded node that is not an end note by 6 has a successor. 10

  15. Tableaux Rules: Extra Conditions 1. On reaching π‘Œ; Β¬[𝐡]𝑄 or π‘Œ; [𝐡]𝑄 , change (π‘œ) back to βˆ— in 𝑄 . 2. Instead of π‘Œ; [𝑏 (π‘œ) ]𝑄 we always obtain π‘Œ . 3. A rule must be applied to an π‘œ -formula whenever it is possible. 4. No rule may be applied to a Β¬[𝑏 (π‘œ) ] -node. 5. To a node obtained using (𝑁+) we may not apply (π‘βˆ’) . path 𝑑 … 𝑒 uses (𝐡𝑒) and is loaded if 𝑑 is loaded, then 𝑒 is an end node. 7. Every loaded node that is not an end note by 6 has a successor. 10 6. If a normal node 𝑒 has a predecessor 𝑑 with the same formulas and the

  16. A Full Proof Example (Β¬π‘œ) x (Β¬?) π‘ž ; Β¬[(𝐡 βˆͺ π‘ž?) x (𝐡𝑒) Β¬[(𝐡 βˆͺ π‘ž?) (Β¬βˆͺ) Β¬[π‘ž?][(𝐡 βˆͺ π‘ž?) (Β¬βˆͺ) Β¬[(𝐡 βˆͺ π‘ž?) Β¬[𝐡][(𝐡 βˆͺ π‘ž?) 11 (𝑁+) x βˆ— ]π‘Ÿ ; [𝐡 βˆ— ]π‘Ÿ (Β¬π‘œ)1. Β¬π‘Ÿ ; π‘Ÿ ; [𝐡][𝐡 βˆ— ]π‘Ÿ Β¬[(𝐡 βˆͺ π‘ž?) (π‘œ) Β¬[(𝐡 βˆͺ π‘ž?)][(𝐡 βˆͺ π‘ž?) Β¬[(𝐡 βˆͺ π‘ž?) βˆ— ]π‘Ÿ π‘Ÿ ; [𝐡 βˆ— ]π‘Ÿ βˆ— ]π‘Ÿ π‘Ÿ ; π‘Ÿ ; [𝐡][𝐡 βˆ— ]π‘Ÿ (π‘œ) ]π‘Ÿ π‘Ÿ ; π‘Ÿ ; [𝐡][𝐡 βˆ— ]π‘Ÿ βˆ— ]π‘Ÿ π‘Ÿ ; π‘Ÿ ; [𝐡][𝐡 βˆ— ]π‘Ÿ (π‘œ) ]π‘Ÿ π‘Ÿ ; π‘Ÿ ; [𝐡][𝐡 βˆ— ]π‘Ÿ π‘Ÿ βˆ— ]π‘Ÿ π‘Ÿ ; [𝐡 βˆ— ] (π‘œ) ]π‘Ÿ π‘Ÿ ; π‘Ÿ ; [𝐡][𝐡 βˆ— ]π‘Ÿ

  17. A Full Proof Example (Β¬π‘œ) closed x (Β¬?) π‘ž ; Β¬[(𝐡 βˆͺ π‘ž?) x (𝐡𝑒) Β¬[(𝐡 βˆͺ π‘ž?) (Β¬βˆͺ) Β¬[π‘ž?][(𝐡 βˆͺ π‘ž?) (Β¬βˆͺ) Β¬[(𝐡 βˆͺ π‘ž?) Β¬[𝐡][(𝐡 βˆͺ π‘ž?) 11 βˆ— ]π‘Ÿ ; [𝐡 βˆ— ]π‘Ÿ x (Β¬π‘œ)1. Β¬[(𝐡 βˆͺ π‘ž?) Β¬π‘Ÿ ; π‘Ÿ ; [𝐡][𝐡 βˆ— ]π‘Ÿ (π‘œ) Β¬[(𝐡 βˆͺ π‘ž?)][(𝐡 βˆͺ π‘ž?) Β¬[(𝐡 βˆͺ π‘ž?) (𝑁+) βˆ— ]π‘Ÿ π‘Ÿ ; [𝐡 βˆ— ]π‘Ÿ βˆ— ]π‘Ÿ π‘Ÿ ; π‘Ÿ ; [𝐡][𝐡 βˆ— ]π‘Ÿ (π‘œ) ]π‘Ÿ π‘Ÿ ; π‘Ÿ ; [𝐡][𝐡 βˆ— ]π‘Ÿ βˆ— ]π‘Ÿ π‘Ÿ ; π‘Ÿ ; [𝐡][𝐡 βˆ— ]π‘Ÿ (π‘œ) ]π‘Ÿ π‘Ÿ ; π‘Ÿ ; [𝐡][𝐡 βˆ— ]π‘Ÿ π‘Ÿ βˆ— ]π‘Ÿ π‘Ÿ ; [𝐡 βˆ— ] (π‘œ) ]π‘Ÿ π‘Ÿ ; π‘Ÿ ; [𝐡][𝐡 βˆ— ]π‘Ÿ

  18. A Full Proof Example (Β¬π‘œ) closed by condition 6 x (Β¬?) π‘ž ; Β¬[(𝐡 βˆͺ π‘ž?) x (𝐡𝑒) Β¬[(𝐡 βˆͺ π‘ž?) (Β¬βˆͺ) Β¬[π‘ž?][(𝐡 βˆͺ π‘ž?) (Β¬βˆͺ) Β¬[(𝐡 βˆͺ π‘ž?) Β¬[𝐡][(𝐡 βˆͺ π‘ž?) 11 βˆ— ]π‘Ÿ ; [𝐡 βˆ— ]π‘Ÿ x (Β¬π‘œ)1. Β¬[(𝐡 βˆͺ π‘ž?) Β¬π‘Ÿ ; π‘Ÿ ; [𝐡][𝐡 βˆ— ]π‘Ÿ (π‘œ) Β¬[(𝐡 βˆͺ π‘ž?)][(𝐡 βˆͺ π‘ž?) Β¬[(𝐡 βˆͺ π‘ž?) (𝑁+) βˆ— ]π‘Ÿ π‘Ÿ ; [𝐡 βˆ— ]π‘Ÿ βˆ— ]π‘Ÿ π‘Ÿ ; π‘Ÿ ; [𝐡][𝐡 βˆ— ]π‘Ÿ (π‘œ) ]π‘Ÿ π‘Ÿ ; π‘Ÿ ; [𝐡][𝐡 βˆ— ]π‘Ÿ βˆ— ]π‘Ÿ π‘Ÿ ; π‘Ÿ ; [𝐡][𝐡 βˆ— ]π‘Ÿ (π‘œ) ]π‘Ÿ π‘Ÿ ; π‘Ÿ ; [𝐡][𝐡 βˆ— ]π‘Ÿ π‘Ÿ βˆ— ]π‘Ÿ π‘Ÿ ; [𝐡 βˆ— ] (π‘œ) ]π‘Ÿ π‘Ÿ ; π‘Ÿ ; [𝐡][𝐡 βˆ— ]π‘Ÿ

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Uniform Interpolation and Proof Systems Rosalie Iemhoff Utrecht University Workshop on

Uniform Interpolation and Proof Systems Rosalie Iemhoff Utrecht University Workshop on

Uniform Interpolation and Proof Systems Rosalie Iemhoff Utrecht University Workshop on Admissible Rules and Unification II Les Diablerets, February 2, 2015 1 / 12 Proof systems An old question: When does a logic have a decent proof system? 2

624 views β€’ 50 slides
Local proof transformations for flexible interpolation and proof reduction N. Sharygina Formal

Local proof transformations for flexible interpolation and proof reduction N. Sharygina Formal

Local proof transformations for flexible interpolation and proof reduction N. Sharygina Formal Verification and Security Group University of Lugano June 21, 2011 Natasha Sharygina (USI) Flexible Proof Transformation June 21, 2011 1 / 72

2.21k views β€’ 186 slides
Part II: Interpolation and Approximation theory Contents: Review of Lagrange interpolation

Part II: Interpolation and Approximation theory Contents: Review of Lagrange interpolation

Part II: Interpolation and Approximation theory Contents: Review of Lagrange interpolation polynomials 1 Newton interpolation 2 Optimal interpolation points; Chebyshev polynomials 3 Cubic spline interpolation 4 Error analysis 5 Numerical

1.14k views β€’ 47 slides
3. Interpolation Closing the Gaps of Discretization . . . 3. Interpolation Numerical Programming

3. Interpolation Closing the Gaps of Discretization . . . 3. Interpolation Numerical Programming

Preliminary Remark Interpolation with Polynomials Polynomial Splines Trigonometric Interpolation Examples for Applications 3. Interpolation Closing the Gaps of Discretization . . . 3. Interpolation Numerical Programming I (for CSE),

616 views β€’ 48 slides
Marcinkiewicz interpolation Updated May 18, 2020 Plan 2 Outline: Interpolation of quasinorms

Marcinkiewicz interpolation Updated May 18, 2020 Plan 2 Outline: Interpolation of quasinorms

Marcinkiewicz interpolation Updated May 18, 2020 Plan 2 Outline: Interpolation of quasinorms Diagonal Marcinkiewicz interpolation theorem General version Applications: Schur test, Hardy-Littlewood-Sobolev Interpolation for quasinorms 3

642 views β€’ 24 slides
3. Interpolation: Closing the Gaps of Discretization . . . 3. Interpolation: Closing the Gaps of

3. Interpolation: Closing the Gaps of Discretization . . . 3. Interpolation: Closing the Gaps of

Preliminary Remark Interpolation with Polynomials Polynomial Splines Trigonometric Interpolation Examples for Applications 3. Interpolation: Closing the Gaps of Discretization . . . 3. Interpolation: Closing the Gaps of Discretization . . .

494 views β€’ 48 slides
A Formalised Proof of Craigs Interpolation Theorem in Nominal Isabelle Peter Chapman Peter

A Formalised Proof of Craigs Interpolation Theorem in Nominal Isabelle Peter Chapman Peter

Introduction Craigs Theorem Formal Proof Further Work A Formalised Proof of Craigs Interpolation Theorem in Nominal Isabelle Peter Chapman Peter Chapman M unchen Talk Introduction Craigs Theorem Formal Proof Further Work

621 views β€’ 59 slides
First-Order Interpolation Laura Kov acs Interpolation: Craig Interpolation Use of

First-Order Interpolation Laura Kov acs Interpolation: Craig Interpolation Use of

First-Order Interpolation Laura Kov acs Interpolation: Craig Interpolation Use of interpolation in software verification thanks to K. McMillan Interpolation: Craig Interpolation Use of interpolation in software verification

1.18k views β€’ 114 slides
Stability and Lebesgue constants in Good interpolation points RBF interpolation Results

Stability and Lebesgue constants in Good interpolation points RBF interpolation Results

Stability and Lebesgue constants in RBF interpolation De Marchi Motivations Stability and Lebesgue constants in Good interpolation points RBF interpolation Results Numerical examples Stability of kernel-based interpolation Stefano De

1.19k views β€’ 78 slides
Interpolation Dr. Mihail October 26, 2015 (Dr. Mihail) Interpolation October 26, 2015 1 / 11

Interpolation Dr. Mihail October 26, 2015 (Dr. Mihail) Interpolation October 26, 2015 1 / 11

Interpolation Dr. Mihail October 26, 2015 (Dr. Mihail) Interpolation October 26, 2015 1 / 11 Definitions 1 Interpolation: method of constructing new data points from sampling or experimentation. (Dr. Mihail) Interpolation October 26, 2015

303 views β€’ 12 slides
WEAK INTERPOLATION PROPERTY over THE MINIMAL LOGIC Larisa Maksimova Sobolev Institute of

WEAK INTERPOLATION PROPERTY over THE MINIMAL LOGIC Larisa Maksimova Sobolev Institute of

Abstract Weak interpolation and joint consistency Propositional J-logics Reduction of WIP Weak interpolation and weak amalgamation Weak interpolation and weak amalgamation Logics with WIP over Gl Description of logics with WIP over Gl and J

621 views β€’ 41 slides
Taylors Series and Interpolation CIS 541 - Interpolation Taylor Series interpolates at a

Taylors Series and Interpolation CIS 541 - Interpolation Taylor Series interpolates at a

Taylors Series and Interpolation CIS 541 - Interpolation Taylor Series interpolates at a specific Roger Crawfis point: The function Its first derivative It may not interpolate at other points. We want an

644 views β€’ 13 slides
On interpolation in theorem proving Maria Paola Bonacina Visiting: Computer Science Laboratory,

On interpolation in theorem proving Maria Paola Bonacina Visiting: Computer Science Laboratory,

Outline Introduction to interpolation Interpolation for propositional resolution Interpolation and equality On interpolation in theorem proving Maria Paola Bonacina Visiting: Computer Science Laboratory, SRI International, Menlo Park, CA, USA

1.65k views β€’ 64 slides
Quantifier elimination, amalgamation, deductive interpolation and Craig interpolation in

Quantifier elimination, amalgamation, deductive interpolation and Craig interpolation in

Quantifier elimination, amalgamation, deductive interpolation and Craig interpolation in many-valued logic Franco Montagna, first part in collaboration with Tommaso Cortonesi and Enrico Marchioni Definition . A logic L has the deductive

380 views β€’ 19 slides
Rod Thompson FIG 3D Cadastres workshop 2-4 October 2018, Delft NL. 1 1988 1988 was the year

Rod Thompson FIG 3D Cadastres workshop 2-4 October 2018, Delft NL. 1 1988 1988 was the year

Rod Thompson FIG 3D Cadastres workshop 2-4 October 2018, Delft NL. 1 1988 1988 was the year the world came to Brisbane Leisure ure in n th the Ag Age of of Te Technology hnology 2 1988 1988 was the year the world came to

752 views β€’ 60 slides
Interpolation CS3220 - Summer 2008 Jonathan Kaldor Interpolation Weve looked at the

Interpolation CS3220 - Summer 2008 Jonathan Kaldor Interpolation Weve looked at the

Interpolation CS3220 - Summer 2008 Jonathan Kaldor Interpolation Weve looked at the problem of model fitting using least squares: given some sample points, determine linear parameters for a model that best fits the data Note:

813 views β€’ 63 slides
Handling Javas Abrupt Termination in a Sequent Calculus for Dynamic Logic Bernhard Beckert

Handling Javas Abrupt Termination in a Sequent Calculus for Dynamic Logic Bernhard Beckert

Handling Javas Abrupt Termination in a Sequent Calculus for Dynamic Logic Bernhard Beckert Bettina Sasse U NIVERSITY OF K ARLSRUHE I NSTITUTE FOR L OGIC , C OMPLEXITY AND D EDUCTION S YSTEMS i12www.ira.uka.de/ key VerifiCard Workshop

604 views β€’ 33 slides
A Logic of Proofs for Differential Dynamic Logic Toward Independently Checkable Proof Certificates

A Logic of Proofs for Differential Dynamic Logic Toward Independently Checkable Proof Certificates

A Logic of Proofs for Differential Dynamic Logic Toward Independently Checkable Proof Certificates for Differential Dynamic Logic Nathan Fulton Andr` e Platzer Carnegie Mellon University CPP16 January 19, 2016 1 Motivation Strong

383 views β€’ 37 slides
Visibly Linear Dynamic Logic Joint work with Alexander Weinert (Saarland University) Martin

Visibly Linear Dynamic Logic Joint work with Alexander Weinert (Saarland University) Martin

Visibly Linear Dynamic Logic Joint work with Alexander Weinert (Saarland University) Martin Zimmermann Saarland University December 14th, 2016 FSTTCS 2016, Chennai, India Martin Zimmermann Saarland University Visibly Linear Dynamic Logic

539 views β€’ 40 slides
Dynamic logics INF5140 Specification and Verification of Parallel Systems Dynamic logics,

Dynamic logics INF5140 Specification and Verification of Parallel Systems Dynamic logics,

Dynamic logics INF5140 Specification and Verification of Parallel Systems Dynamic logics, lecture 3 Spring 2015 February 24, 2015 2 / 21 Introduction Problem FOL is very (at leat relative) expressive but undecidable. Good for

380 views β€’ 21 slides
Individual Voltage Scaling in Logic and Memory Circuits towards Runtime Energy Optimization in

Individual Voltage Scaling in Logic and Memory Circuits towards Runtime Energy Optimization in

Individual Voltage Scaling in Logic and Memory Circuits towards Runtime Energy Optimization in Processors Jun Shiomi, Tohru Ishihara, Hidetoshi Onodera Graduate School of Informatics, Kyoto University, Japan 1 Energy Reduction by Dynamic

556 views β€’ 21 slides
The Surprise Examination Paradox in Dynamic Epistemic Logic Alexandru Marcoci ESSLLI 2010

The Surprise Examination Paradox in Dynamic Epistemic Logic Alexandru Marcoci ESSLLI 2010

The Surprise Examination Paradox in Dynamic Epistemic Logic Alexandru Marcoci ESSLLI 2010 Workshop: Logic, Rationality, Interaction August 17, 2010 Alexandru Marcoci The Surprise Examination Paradox in DEL Introduction SEP has widely been

549 views β€’ 36 slides
Propositional Dynamic Logic With Belnapian Truth Values Igor Sedlr Institute of Computer

Propositional Dynamic Logic With Belnapian Truth Values Igor Sedlr Institute of Computer

Propositional Dynamic Logic With Belnapian Truth Values Igor Sedlr Institute of Computer Science, Czech Academy of Sciences, Prague AiML 2016, Budapest, 31 August 2016 Overview BPDL , a four-valued paraconsistent version of propositional dy-

462 views β€’ 23 slides
KeYmaera: A Hybrid Theorem Prover for Hybrid Systems Andr e Platzer Jan-David Quesel

KeYmaera: A Hybrid Theorem Prover for Hybrid Systems Andr e Platzer Jan-David Quesel

KeYmaera: A Hybrid Theorem Prover for Hybrid Systems Andr e Platzer Jan-David Quesel University of Oldenburg, Department of Computing Science, Germany International Joint Conference on Automated Reasoning, Sydney 2008 Andr e Platzer,

533 views β€’ 25 slides

More recommend