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### PDL with negation of atomic programs

Carsten Lutz, Dirk Walther
2005 Journal of Applied Non-Classical Logics
In this paper, we consider the extension of PDL with negation of atomic programs, only.  ...  A very natural and useful such extension is with negation of programs. Unfortunately, as long-known, reasoning with the resulting logic is undecidable.  ...  PDL with Negation In this section, we introduce propositional dynamic logic (PDL) with negation of programs. We start with defining full PDL ¬ , i.e.  ...

### PDL with Negation of Atomic Programs [chapter]

Carsten Lutz, Dirk Walther
2004 Lecture Notes in Computer Science
In this paper, we consider the extension of PDL with negation of atomic programs, only.  ...  A very natural and useful such extension is with negation of programs. Unfortunately, as long-known, reasoning with the resulting logic is undecidable.  ...  PDL with Negation In this section, we introduce propositional dynamic logic (PDL) with negation of programs. We start with defining full PDL ¬ , i.e.  ...

### Preferences and Priorities in ASP

Stefania Costantini, Andrea Formisano
2012 Italian Conference on Computational Logic
In this paper we extend our previous work concerning preferences in Answer Set Programming (ASP), and integrate this work with PDL, a wellknown approach to answer set optimization.  ...  each L i is either an atom or the classical negation (also called strong negation) of an atom (as defined in [18] ).  ...  Finally, in Section 6 we conclude. 2 Background on ASP and PDL Answer Set Programming is the well-established logic programming paradigm adopting Datalog programs with default negation under the answer  ...

### Probabilistic Description Logic Programs [chapter]

Thomas Lukasiewicz
2005 Lecture Notes in Computer Science
Such dl-rules are similar to usual rules in logic programs with negation as failure, but may also contain queries to L in their bodies, which are given by special atoms (on which possibly default negation  ...  programs (or pdl-programs), which are a combination of description logic programs (or dl-programs) under the answer set semantics and the well-founded semantics with Poole's independent choice logic.  ...  Conclusion We have presented probabilistic dl-programs (or pdl-programs), which are a combination of dl-programs under the answer set and the well-founded semantics with Poole's independent choice logic  ...

### Probabilistic description logic programs

Thomas Lukasiewicz
2007 International Journal of Approximate Reasoning
Such dl-rules are similar to usual rules in logic programs with negation as failure, but may also contain queries to L in their bodies, which are given by special atoms (on which possibly default negation  ...  programs (or pdl-programs), which are a combination of description logic programs (or dl-programs) under the answer set semantics and the well-founded semantics with Poole's independent choice logic.  ...  Conclusion We have presented probabilistic dl-programs (or pdl-programs), which are a combination of dl-programs under the answer set and the well-founded semantics with Poole's independent choice logic  ...

### Equational axioms of test algebra [chapter]

Marco Hollenberg
1998 Lecture Notes in Computer Science
The main idea is adding dynamic negation ( 9, 2, 11]) to the signature of Kleene algebras, that turns any program into a test whether this program cannot succeed with the current state as input.  ...  The axiomatization of test algebra is arrived at by adding a nite number of equations to a necessarily in nite or rule-based axiomatization of Kleene algebra combined with algebraic PDL-axioms.  ...  Frederick Smith, Hajnal Andr eka, Jan Bergstra, Luca Aceto and Albert Visser (in no particular order) for encouraging and aiding me in this research, and actually reading unreadable earlier versions of  ...

### Sequential Dynamic Logic

Alexander Bochman, Dov M. Gabbay
2011 Journal of Logic, Language and Information
Completeness of the calculus with respect to the intended relational semantics is established.  ...  propositional dynamic logic (PDL).  ...  From SDL to PDL. To begin with, the following translation transforms any SDL-formula into a program of PDL: δ(π) = π δ(p) =?p δ(A ∧ B) = δ(A); δ(B) δ(∼A) =?  ...

### Model checking propositional dynamic logic with all extras

Martin Lange
2006 Journal of Applied Logic
This paper presents a model checking algorithm for Propositional Dynamic Logic (PDL) with looping, repeat, test, intersection, converse, program complementation as well as context-free programs.  ...  The algorithm shows that the model checking problem for PDL remains PTIME-complete in the presence of all these operators, in contrast to the high increase in complexity that they cause for the satisfiability  ...  The negation operator forms the complement of a program.  ...

### Page 3555 of Mathematical Reviews Vol. , Issue 83i [page]

1983 Mathematical Reviews
It seems from the proof that a DPDL model is a PDL model in which the meanings of atomic programs are not relations but functions.  ...  In the notation of the paper this means that a PDL model S is a DPDL model if and only if (A) , is a function for every atomic program A (see p. 230).  ...

### Conflict resolution using logic programming

J. Chomicki, J. Lobo, S. Naqvi
2003 IEEE Transactions on Knowledge and Data Engineering
We use a declarative policy description language PDL, in which policies are formulated as sets of ECA rules.  ...  The semantics of rules and conflict detection and resolution are defined axiomatically using logic programs.  ...  The input epoch of a monitor is specified using occ atoms, the output of the policy using exec atoms, and the output of a monitor using accept atoms.  ...

### Undecidability of PDL with L = {a2i |; i ⩾ 0}

D. Harel, M.S. Paterson
1984 Journal of computer and system sciences (Print)
It is shown that the validity problem for propositional dynamic logic (PDL), which is decidable and actually DEXPTIME-complete for the usual class of regular programs, becomes highly undecidable, viz.  ...  This answers a question of Harel, Pnueli, and Stavi. 0 1984 Academic Press, Inc.  ...  UNDECIDABILITY OF PDL WITH I!, = (u" 1 i > o}  ...

### Computation paths logic: An expressive, yet elementary, process logic

David Harel, Eli Singerman
1999 Annals of Pure and Applied Logic
CPL is a pathwlse extension of PDL. following the basic pt-ocess logic of Harel. Kozen and Parikh. and is close in spirit to the logic R of Hare1 and Peleg.  ...  A new process logic is defined, called computation paths logic (CPL). which treats lbnn~~la~ and programs essentially alike.  ...  In SICPL, interleaving can be synchronized with respect to subsets of atomic programs.  ...

### Reasoning in Expressive Description Logics [chapter]

Diego Calvanese, Giuseppe De Giacomo, Daniele Nardi, Maurizio Lenzerini
2001 Handbook of Automated Reasoning
We denote propositional letters with A, arbitrary formulas with φ, atomic programs with P , and arbitrary programs with r, all possibly with subscripts.  ...  or negated atomic concept.  ...  µ-calculus, 46 n-ary relation, 44 negation, 7 negation normal form, 23 number restriction, 7, 43 PDL, 15, 19, 25 PDLs, 13, 15, 19, 25, 40  ...

### Completeness and decidability of converse PDL in the constructive type theory of Coq

Christian Doczkal, Joachim Bard
2018 Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs - CPP 2018
Completeness of Segerberg's axiomatization of PDL is then obtained by translating pruning refutations to derivations in the Hilbert system.  ...  We first treat PDL without converse and then extend the proofs to Converse PDL. All results are formalized in Coq/Ssreflect.  ...  This work was supported by the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program łInvestissements d'Avenirž (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR  ...

### Specification and Execution of Declarative Policies for Grid Service Selection [chapter]

Massimo Marchi, Alessandra Mileo, Alessandro Provetti
2004 Lecture Notes in Computer Science
PPDL policies are evaluated by translating them into a Logic Program with Ordered Disjunctions and calling the psmodels interpreter.  ...  We describe a modified Grid architecture that allows to specify and enforce connection policies with preferences and integrity constraints.  ...  The answer sets of a LPODs program are defined by Brewka as sets of atoms that maximize a preference relation induced by the "×-rules" of the program.  ...
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