Multi-type display calculus for propositional dynamic logic

We introduce a multi-type display calculus for Propositional Dynamic Logic (PDL). This calculus is complete w.r.t. PDL, and enjoys Belnap-style cut-elimination and subformula property.

[1]  Vaughan R. Pratt,et al.  Action Logic and Pure Induction , 1990, JELIA.

[2]  Willem Conradie,et al.  Unified Correspondence , 2014, Johan van Benthem on Logic and Information Dynamics.

[3]  Francesca Poggiolesi,et al.  Gentzen Calculi for Modal Propositional Logic , 2010 .

[4]  Chrysafis Hartonas,et al.  On the Dynamic Logic of Agency and Action , 2013, Studia Logica.

[5]  Rajeev Goré,et al.  Substructural Logics on Display , 1998, Log. J. IGPL.

[6]  Alessandra Palmigiano,et al.  A proof-theoretic semantic analysis of dynamic epistemic logic , 2016, J. Log. Comput..

[7]  Richard E. Ladner,et al.  Propositional Dynamic Logic of Regular Programs , 1979, J. Comput. Syst. Sci..

[8]  Rajeev Goré,et al.  From Display Calculi to Deep Nested Sequent Calculi: Formalised for Full Intuitionistic Linear Logic , 2014, IFIP TCS.

[9]  Robert Goldblatt,et al.  Parallel action: Concurrent dynamic logic with independent modalities , 1992, Stud Logica.

[10]  Nuel Belnap,et al.  Display logic , 1982, J. Philos. Log..

[11]  Angus Macintyre,et al.  Trends in Logic , 2001 .

[12]  Willem Conradie,et al.  Algorithmic correspondence for intuitionistic modal mu-calculus , 2015, Theor. Comput. Sci..

[13]  Ulle Endriss,et al.  SAHLQVIST CORRESPONDENCE FOR INTUITIONISTIC MODAL MU-CALCULUS , 2013 .

[14]  H. Wansing.  Displaying Modal Logic , 1998 .

[15]  Jerzy Tiuryn,et al.  Dynamic logic , 2001, SIGA.

[16]  Nuel Belnap,et al.  Gupta's rule of revision theory of truth , 1982, J. Philos. Log..

[17]  Rohit Parikh,et al.  An Elementary Proof of the Completness of PDL , 1981, Theor. Comput. Sci..

[18]  B. Davey,et al.  Introduction to Lattices and Order: Appendix B: further reading , 2002 .

[19]  Chrysafis Hartonas,et al.  Reasoning about types of action and agent capabilities , 2013, Log. J. IGPL.

[20]  Pedro Resende,et al.  Lectures on etale groupoids, inverse semigroups and quantales , 2010 .

[21]  K. Segerberg.  A completeness theorem in the modal logic of programs , 1982 .

[22]  Chrysafis Hartonas,et al.  Analytic Cut for Propositional Dynamic Logic , 2010 .

[23]  Willem Conradie,et al.  Algebraic modal correspondence: Sahlqvist and beyond , 2016, J. Log. Algebraic Methods Program..

[24]  Alessandra Palmigiano,et al.  Multi-type Sequent Calculi , 2016 .

[25]  Rajeev Goré,et al.  Annotation-Free Sequent Calculi for Full Intuitionistic Linear Logic - Extended Version , 2013, CSL.

[26]  Yde Venema,et al.  Dynamic Logic by David Harel, Dexter Kozen and Jerzy Tiuryn. The MIT Press, Cambridge, Massachusetts. Hardback: ISBN 0–262–08289–6, $50, xv + 459 pages , 2002, Theory and Practice of Logic Programming.

[27]  Willem Conradie,et al.  Algorithmic correspondence and canonicity for distributive modal logic , 2012, Ann. Pure Appl. Log..

[28]  Alessandra Palmigiano,et al.  Multi-type display calculus for dynamic epistemic logic , 2016, J. Log. Comput..