52,597 research outputs found
Normalization in Supernatural deduction and in Deduction modulo
Deduction modulo and Supernatural deduction are two extentions of predicate logic with computation rules. Whereas the application of computation rules in deduction modulo is transparent, these rules are used to build non-logical deduction rules in Supernatural deduction. In both cases, adding computation rules may jeopardize proof normalization, but various conditions have been given in both cases, so that normalization is preserved. We prove in this paper that normalization in Supernatural deduction and in Deduction modulo are equivalent, i.e. the set of computation rules for which one system strongly normalizes is the same as the set of computation rules for which the other is
Strategic Computation and Deduction
We introduce the notion of abstract strategies for abstract reduction systems. Adequate properties of termination, confluence and normalization under strategy can then be defined. Thanks to this abstract concept, we draw a parallel between strategies for computation and strategies for deduction. We define deduction rules as rewrite rules, a deduction step as a rewriting step and a proof construction step as a narrowing step in an adequate abstract reduction system. Computation, deduction and proof search are thus captured in the uniform foundational concept of abstract reduction system in which abstract strategies have a clear formalisation
Automated Generation of User Guidance by Combining Computation and Deduction
Herewith, a fairly old concept is published for the first time and named
"Lucas Interpretation". This has been implemented in a prototype, which has
been proved useful in educational practice and has gained academic relevance
with an emerging generation of educational mathematics assistants (EMA) based
on Computer Theorem Proving (CTP).
Automated Theorem Proving (ATP), i.e. deduction, is the most reliable
technology used to check user input. However ATP is inherently weak in
automatically generating solutions for arbitrary problems in applied
mathematics. This weakness is crucial for EMAs: when ATP checks user input as
incorrect and the learner gets stuck then the system should be able to suggest
possible next steps.
The key idea of Lucas Interpretation is to compute the steps of a calculation
following a program written in a novel CTP-based programming language, i.e.
computation provides the next steps. User guidance is generated by combining
deduction and computation: the latter is performed by a specific language
interpreter, which works like a debugger and hands over control to the learner
at breakpoints, i.e. tactics generating the steps of calculation. The
interpreter also builds up logical contexts providing ATP with the data
required for checking user input, thus combining computation and deduction.
The paper describes the concepts underlying Lucas Interpretation so that open
questions can adequately be addressed, and prerequisites for further work are
provided.Comment: In Proceedings THedu'11, arXiv:1202.453
A generic framework for the analysis and specialization of logic programs
The relationship between abstract interpretation and partial
deduction has received considerable attention and (partial) integrations have been proposed starting from both the partial deduction and abstract interpretation perspectives. In this work we present what we argüe is the first fully described generic algorithm for efñcient and precise integration of abstract interpretation and partial deduction. Taking as starting point state-of-the-art algorithms for context-sensitive, polyvariant abstract interpretation and (abstract) partial deduction, we present
an algorithm which combines the best of both worlds. Key ingredients include the accurate success propagation inherent to abstract interpretation and the powerful program transformations achievable by partial deduction. In our algorithm, the calis which appear in the analysis graph
are not analyzed w.r.t. the original definition of the procedure but w.r.t. specialized definitions of these procedures. Such specialized definitions are obtained by applying both unfolding and abstract executability. Our framework is parametric w.r.t. different control strategies and abstract domains. Different combinations of such parameters correspond to existing algorithms for program analysis and specialization. Simultaneously, our approach opens the door to the efñcient computation of strictly more
precise results than those achievable by each of the individual techniques.
The algorithm is now one of the key components of the CiaoPP analysis
and specialization system
Confluence Competition 2018
We report on the 2018 edition of the Confluence Competition, a competition of software tools that aim to (dis)prove confluence and related properties of rewrite systems automatically
Decidability of Univariate Real Algebra with Predicates for Rational and Integer Powers
We prove decidability of univariate real algebra extended with predicates for
rational and integer powers, i.e., and . Our decision procedure combines computation over real algebraic
cells with the rational root theorem and witness construction via algebraic
number density arguments.Comment: To appear in CADE-25: 25th International Conference on Automated
Deduction, 2015. Proceedings to be published by Springer-Verla
Integrating multiple sources to answer questions in Algebraic Topology
We present in this paper an evolution of a tool from a user interface for a
concrete Computer Algebra system for Algebraic Topology (the Kenzo system), to
a front-end allowing the interoperability among different sources for
computation and deduction. The architecture allows the system not only to
interface several systems, but also to make them cooperate in shared
calculations.Comment: To appear in The 9th International Conference on Mathematical
Knowledge Management: MKM 201
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