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PDL with negation of atomic programs
2005
Journal of Applied Non-Classical Logics
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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. ...
doi:10.3166/jancl.15.189-213
fatcat:7yhetwfn2bgj5iopwisey2apm4
PDL with Negation of Atomic Programs
[chapter]
2004
Lecture Notes in Computer Science
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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. ...
doi:10.1007/978-3-540-25984-8_18
fatcat:a4axkpousze7bke7vado37c4y4
Preferences and Priorities in ASP
2012
Italian Conference on Computational Logic
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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 ...
dblp:conf/cilc/CostantiniF12
fatcat:xmmz7uvbsvgi7ettjt3gougc5m
Probabilistic Description Logic Programs
[chapter]
2005
Lecture Notes in Computer Science
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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 ...
doi:10.1007/11518655_62
fatcat:2fkh2ijkubhslezjjurq2c3ak4
Probabilistic description logic programs
2007
International Journal of Approximate Reasoning
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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 ...
doi:10.1016/j.ijar.2006.06.012
fatcat:uwt4uvjzszhula5jh5tzmewz4u
Equational axioms of test algebra
[chapter]
1998
Lecture Notes in Computer Science
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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 ...
doi:10.1007/bfb0028021
fatcat:dk5p5e56y5dzjmw7fqxe7xgetm
Sequential Dynamic Logic
2011
Journal of Logic, Language and Information
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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) =? ...
doi:10.1007/s10849-011-9152-y
fatcat:dphgfgdbxbgapkfluwprzlzpqq
Model checking propositional dynamic logic with all extras
2006
Journal of Applied Logic
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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. ...
doi:10.1016/j.jal.2005.08.002
fatcat:a733vgxnznhxvodpnexswof44a
Page 3555 of Mathematical Reviews Vol. , Issue 83i
[page]
1983
Mathematical Reviews
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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
2003
IEEE Transactions on Knowledge and Data Engineering
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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. ...
doi:10.1109/tkde.2003.1161596
fatcat:5er5qxa47baqtjn7hp4ikmi6zq
Undecidability of PDL with L = {a2i |; i ⩾ 0}
1984
Journal of computer and system sciences (Print)
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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} ...
doi:10.1016/0022-0000(84)90005-9
fatcat:f7udt723qvapddi7nllcfp4npe
Computation paths logic: An expressive, yet elementary, process logic
1999
Annals of Pure and Applied Logic
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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. ...
doi:10.1016/s0168-0072(98)00038-4
fatcat:4ckozyoo2fddla7ucnhzl6oapq
Reasoning in Expressive Description Logics
[chapter]
2001
Handbook of Automated Reasoning
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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 ...
doi:10.1016/b978-044450813-3/50025-4
fatcat:v5bdkikn7bhipjgeqh4z3mxixm
Completeness and decidability of converse PDL in the constructive type theory of Coq
2018
Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs - CPP 2018
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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 ...
doi:10.1145/3167088
dblp:conf/cpp/DoczkalB18
fatcat:3i24ickb4bfsdjkxdgrtw74wsu
Specification and Execution of Declarative Policies for Grid Service Selection
[chapter]
2004
Lecture Notes in Computer Science
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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. ...
doi:10.1007/978-3-540-30209-4_8
fatcat:6yupfb6c7jgdvbt5prpv2jbuyu
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