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Propositional dynamic logic of flowcharts [chapter]

D. Harel, R. Sherman
1983 Lecture Notes in Computer Science  
Following a suggestion of Pratt, we consider propositional dynamic logic in which programs are nondeterministic finite automata o~¢er atomic programs and tests (i.e., flowcharts), rather than regular expressions  ...  We present an elementary combined proof of the completeness of a simple axiom system for APDL and decidability of the validity problem in exponential time.  ...  Pnueli suggested an important improvement in the structure of the main proof.  ... 
doi:10.1007/3-540-12689-9_104 fatcat:mwgdwhmaovafrmny3mqls7sfw4

Propositional dynamic logic of flowcharts

D. Harel, R. Sherman
1985 Information and Control  
Following a suggestion of Pratt, we consider propositional dynamic logic in which programs are nondeterministic finite automata o~¢er atomic programs and tests (i.e., flowcharts), rather than regular expressions  ...  We present an elementary combined proof of the completeness of a simple axiom system for APDL and decidability of the validity problem in exponential time.  ...  Pnueli suggested an important improvement in the structure of the main proof.  ... 
doi:10.1016/s0019-9958(85)80047-4 fatcat:bpnepzglu5hcxpb7gvrhmhyi6e

Cumulative subject index volumes 56–59

1983 Information and Control  
of sentences in, satisfiability problem for, 59, 1 Proportional sentences class, satisfiability problem for, 59, 1 Propositional dynamic logic model, and process logic, 57, 56 Propositional temporal  ...  regular: not interpretable in deter- ministic context-free dynamic logic, 59, 94 process, and propositional dynamic logic model, 57, 56 proportional, class of sentences in: satisfiability problem  ... 
doi:10.1016/s0019-9958(83)80037-0 fatcat:dtwnjwpfbndyfc26jagdqcnmwa

Page 6189 of Mathematical Reviews Vol. , Issue 91K [page]

1991 Mathematical Reviews  
For this purpose, a logic of total correctness of programs is introduced, which is an extension of a predicate logic and a variant of Pratt’s dynamic logic equipped with program vari- ables.  ...  The main technical point is a calcu- lus for isomorphism classes of flowchart schemes.  ... 

Page 2760 of Mathematical Reviews Vol. , Issue 85g [page]

1985 Mathematical Reviews  
(IL-WEIZ) Propositional dynamic logic of flowcharts. Foundations of computation theory (Borgholm, 1983), 195-206, Lecture Notes in Comput. Sci., 158, Springer, Berlin-New York, 1983.  ...  Pratt, we consider propositional dynamic logic in which programs are non- deterministic finite automata over atomic programs and tests (i.e., flowcharts), rather than regular expressions.  ... 

Cumulative subject index volumes 64–67

1985 Information and Control  
, 67, 23 F Flowcharts propositional dynamic logic, 64, 119 Formulas correctness, and equivalence problem, for simple loop programs, 65, 18 G Grammars commutative, computational complexity  ...  , 67, 12 Hoare's logic, relative completeness, 66, 29 Lattices countable distributive, embedding in polynomial time degree intervals, 65, 63 Logic dynamic, see Dynamic logic with fixed-point or  ... 
doi:10.1016/s0019-9958(85)80038-3 fatcat:cnfpoerj4bgahkwbjf5nrkty5e

Flowcharting the Meaning of Logic Formulas

Sabah Al-Fedaghi
2016 International Journal of Advanced Research in Artificial Intelligence (IJARAI)  
Current diagrammatic representations of logic formulas do not completely depict their underlying semantics, and they lack a basic static structure that incorporates elementary dynamic features, creating  ...  In logic, representation of a domain (e.g., physical reality) comprises the things its expressions (formulas) refer to and their relationships.  ...  FM AS A LOGIC LANGUAGE Current visualization methods for logic language are not clear on basic static and dynamic features, creating a conceptual gap that can lead to misinterpretation [18] [19] [20]  ... 
doi:10.14569/ijarai.2016.051005 fatcat:j2xdwpkwnjaivbuzpkhehxf7xu

Page 6557 of Mathematical Reviews Vol. , Issue 87k [page]

1987 Mathematical Reviews  
(IL-WEIZ) Propositional dynamic logic of flowcharts. Inform. and Control 64 (1985), no. 1-3, 119-135.  ...  In propositional dynamic logic (PDL), programs are regular ex- pressions over atomic programs and tests.  ... 

Page 2122 of Mathematical Reviews Vol. , Issue 83e [page]

1983 Mathematical Reviews  
In this paper it is shown that propositional dynamic logic (PDL) has more expressive power than PDL, (PDL without the test symbol “?”).  ...  Berman, Francine; Paterson, Michael Propositional dynamic logic is weaker without tests. Theoret. Comput. Sci. 16 (1981), no. 3, 321-328.  ... 

Page 434 of Mathematical Reviews Vol. , Issue 87a [page]

1987 Mathematical Reviews  
Author summary: “We consider variants of propositional dynamic logic (PDL) augmented with the converse construct.  ...  Author summary: “Over many familiar data types the notion of ‘computable’ coincides with the notion offlowchartable’.  ... 

Page 3839 of Mathematical Reviews Vol. , Issue 87g [page]

1987 Mathematical Reviews  
Propositional mu-calculus is a logic which permits reasoning about program properties. It subsumes propositional dynamic logic (PDL) as well as some of its variants, such as repeat-PDL and loop-PDL.  ...  Iréne Guessarian (Paris) Streett, Robert S. (1-BOST) 87g:68049 Fixpoints and program looping: reductions from the propositional mu-calculus into propositional dynamic logics of looping.  ... 

Dynamic algebras: Examples, constructions, applications

Vaughan Pratt
1991 Studia Logica: An International Journal for Symbolic Logic  
Applications include a new completeness proof for the Segerberg axiomatization of propositional dynamic logic, and yet another notion of regular algebra.  ...  Using this result we give several examples of dynamic algebras arising naturally in connection with additive functions, binary relations, state trajectories, languages, and flowcharts.  ...  Kozen was a most helpful source of ideas and pointers into the literature. J. Halpern provided many helpful comments on an early draft of the paper. Comments of I. Németi and D.  ... 
doi:10.1007/bf00370685 fatcat:bfbvz2yb5jbvnnb5cd6rdqf2mi

Program Analysis and Verification Based on Kleene Algebra in Isabelle/HOL [chapter]

Alasdair Armstrong, Georg Struth, Tjark Weber
2013 Lecture Notes in Computer Science  
We apply this formalisation to a complex flowchart transformation proof from the literature. We extend SKAT with assertion statements and derive the inference rules of Hoare logic.  ...  Schematic Kleene algebra with tests (SKAT) supports the equational verification of flowchart scheme equivalence and captures simple while-programs with assignment statements.  ...  The latter are algebraic relatives of propositional dynamic logic.  ... 
doi:10.1007/978-3-642-39634-2_16 fatcat:bzxg2fl7i5gvfevgx444jsuwgy

Intuitionistic Ancestral Logic as a Dependently Typed Abstract Programming Language [chapter]

Liron Cohen, Robert L. Constable
2015 Lecture Notes in Computer Science  
While it is quite common to identify 'logic' with 'first-order logic' (F OL), a careful examination of the various applications of logic in computer science reveals that F OL is insufficient for most of  ...  It is well-known that concepts and methods of logic (more specifically constructive logic) occupy a central place in computer science.  ...  This research was partially supported by the Ministry of Science, Technology and Space, Israel, and the Cornell University PRL Group.  ... 
doi:10.1007/978-3-662-47709-0_2 fatcat:hkiwoliilvcfjnj7ogpwkkktyu

TEACHING MATHEMATICS WITH PIAGET'S THEORY

Ega Gradini
2013 Visipena  
way of thinking in mathematics learning.  ...  Below, there is first a short description of Piaget's views about the nature of intelligence and then a description of the stages through which it develops until maturity.This paper presented student's  ...  The operations from set theory were translated into logical connectives. Truth tables were done with three independent propositions.  ... 
doi:10.46244/visipena.v4i1.98 fatcat:kbpttocqlzfafpa2aidom5s2vq
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