A Canonical Model Construction for Iteration-Free PDL with Intersection
نویسندگان
چکیده
We study the axiomatisability of the iteration-free fragment of Propositional Dynamic Logic with Intersection and Tests. The combination of program composition, intersection and tests makes its proof-theory rather difficult. We develop a normal form for formulae which minimises the interaction between these operators, as well as a refined canonical model construction. From these we derive an axiom system and a proof of its strong completeness.
منابع مشابه
Eliminating Unorthodox Derivation Rules in an Axiom System for Iteration-free PDL with Intersection
We devote this paper to the completeness of an axiom system for PDL0 — a variant of PDL which includes the program operations of composition and intersection. Most of the difficulty in the proof of the completeness theorem for PDL0 lies in the fact that intersection of accessibility relations is not modally definable. We overcome this difficulty by considering the concepts of theory and large p...
متن کاملWeak Completeness of Coalgebraic Dynamic Logics
We present a coalgebraic generalisation of Fischer and Ladner’s Propositional Dynamic Logic (PDL) and Parikh’s Game Logic (GL). In earlier work, we proved a generic strong completeness result for coalgebraic dynamic logics without iteration. The coalgebraic semantics of such programs is given by a monad T , and modalities are interpreted via a predicate lifting λ whose transpose is a monad morp...
متن کاملModel checking propositional dynamic logic with all extras
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 satisfia...
متن کاملPDL with Intersection and Converse is 2EXP-complete
We study the complexity of satisfiability in the expressive extension ICPDL of PDL (Propositional Dynamic Logic), which admits intersection and converse as program operations. Our main result is containment in 2EXP, which improves the previously known non-elementary upper bound and implies 2EXPcompleteness due to an existing lower bound for PDL with intersection. The proof proceeds by showing t...
متن کاملNONDET~IIi~ISTiC PROPOSITIONAL DYNAMIC LOGIC ~ITH II~T~Q~ECTION IS DECIDABLE
Propositional Dynamic Logic (PDL) of [FL] defines meaning of programs in terms of binary input-output relations. Basic regular operations on programs are interpreted as superposition, union, and reflexive-transitive closure of relations. The intersection, cf. [HI , is a binary program forming functor a~b with the meaning given by the set-theoretical intersection of relations corresponding to pr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016