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Induction of Non-Monotonic Logic Programs to Explain Boosted Tree Models Using LIME [article]

Farhad Shakerin, Gopal Gupta
2018 arXiv   pre-print
Then, in order to explain the model's global behavior, we propose the LIME-FOLD algorithm ---a heuristic-based inductive logic programming (ILP) algorithm capable of learning non-monotonic logic programs  ...  We present a heuristic based algorithm to induce nonmonotonic logic programs that will explain the behavior of XGBoost trained classifiers.  ...  The LIME-FOLD algorithm learns a non-monotonic logic program from the transformed data set. This logic program explains the global behavior of the model.  ... 
arXiv:1808.00629v2 fatcat:qivoa474arh4fa2qehfm3iymti

A study of relevance for learning in deductive databases

Nada Lavrač, Dragan Gamberger, Viktor Jovanoski
1999 The Journal of Logic Programming  
A simple inductive logic programming (ILP) problem is used to illustrate the approach to irrelevant literal and example elimination.  ...  It gives definitions of irrelevant literals and irrelevant examples and presents ecient algorithms that enable their elimination.  ...  This work has been ®nancially supported by the Slovenian Ministry of Science and Technology, the Croatian Ministry of Science, and the ESPRIT project 20237 Inductive Logic Programming 2.  ... 
doi:10.1016/s0743-1066(99)00019-9 fatcat:dchqvpvekrdbjju7kz3yppuz2q

Curry without Success

Sergio Antoy, Michael Hanus
2014 Workshop Logische Programmierung  
Curry is a successful, general-purpose, functional logic programming language that predefines a singleton type Success explicitly to support its logic component.  ...  in Haskell.  ...  Nevertheless, the logic programming features, like non-determinism and evaluating functions with unknown arguments, are still applicable with our new semantics.  ... 
dblp:conf/wlp/AntoyH14 fatcat:5mpbeoc63jh7zgkzgodx56euri

Synthesizing proofs from programs in the Calculus of Inductive Constructions [chapter]

Catherine Parent
1995 Lecture Notes in Computer Science  
In type theory, a proof can be represented as a typed -term Con86, NPS90]. There exist methods to mark logical parts in proofs and extract their algorithmic contents.  ...  Abstract In type theory, a proof can be represented as a typed -term Con86, NPS90]. There exist methods to mark logical parts in proofs and extract their algorithmic contents.  ...  There are two kinds of eliminations : the dependent elimination (Dep(s; s 0 )) and the non-dependent elimination (Nodep(s; s 0 )). The non-dependent one is a particular case of the dependent one.  ... 
doi:10.1007/3-540-60117-1_20 fatcat:fx2m63lrundwhpity6xtf4jvm4

Integrating Linear and Dependent Types

Neelakantan R. Krishnaswami, Pierre Pradic, Nick Benton
2015 Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL '15  
In the linear/non-linear (LNL) calculus, we no longer have to view the intuitionistic function space P → Q through the lens of the Girard encoding !P Q.  ...  However, one stillmissing feature of program logics is support of logical variables. These are variables which occur only in specifications, but which do not affect the evaluation of a program.  ... 
doi:10.1145/2676726.2676969 dblp:conf/popl/KrishnaswamiPB15 fatcat:3sswpdyi4ngdroooaqcqyvnqhm

Integrating Linear and Dependent Types

Neelakantan R. Krishnaswami, Pierre Pradic, Nick Benton
2015 SIGPLAN notices  
In the linear/non-linear (LNL) calculus, we no longer have to view the intuitionistic function space P → Q through the lens of the Girard encoding !P Q.  ...  However, one stillmissing feature of program logics is support of logical variables. These are variables which occur only in specifications, but which do not affect the evaluation of a program.  ... 
doi:10.1145/2775051.2676969 fatcat:k74ipqhvlvgt5fzww7zajmaayy

Effective interactive proofs for higher-order imperative programs

Adam Chlipala, Gregory Malecha, Greg Morrisett, Avraham Shinnar, Ryan Wisnesky
2009 Proceedings of the 14th ACM SIGPLAN international conference on Functional programming - ICFP '09  
Compared to competing approaches to data structure verification, our system includes much less code that must be trusted; namely, about a hundred lines of Coq code defining a program logic.  ...  The core of the automation is a simplification procedure for implications in higher-order separation logic, with hooks that allow programmers to add domain-specific simplification rules.  ...  We prove that a functional list related to a non-null pointer decomposes in the expected way.  ... 
doi:10.1145/1596550.1596565 dblp:conf/icfp/ChlipalaMMSW09 fatcat:qc5rox6vt5bchijlgkp6sw4ckm

Effective interactive proofs for higher-order imperative programs

Adam Chlipala, Gregory Malecha, Greg Morrisett, Avraham Shinnar, Ryan Wisnesky
2009 SIGPLAN notices  
Compared to competing approaches to data structure verification, our system includes much less code that must be trusted; namely, about a hundred lines of Coq code defining a program logic.  ...  The core of the automation is a simplification procedure for implications in higher-order separation logic, with hooks that allow programmers to add domain-specific simplification rules.  ...  We prove that a functional list related to a non-null pointer decomposes in the expected way.  ... 
doi:10.1145/1631687.1596565 fatcat:2dayvkbzdza53ge7eypfv3iq3e

Definitional proof-irrelevance without K

Gaëtan Gilbert, Jesper Cockx, Matthieu Sozeau, Nicolas Tabareau
2019 Proceedings of the ACM on Programming Languages (PACMPL)  
In this paper, taking inspiration from homotopy type theory, we propose a general way to extend a type theory with definitional proof irrelevance, in a way that keeps type checking decidable and is compatible  ...  We provide a new criterion to decide whether a proposition can be eliminated over a type (correcting and improving the so-called singleton elimination of Coq) by using techniques coming from recent development  ...  The idea there is to mark in the function type which arguments can be considered as irrelevant.  ... 
doi:10.1145/3290316 fatcat:5fjmdnyz3fbgnfacrydnjjhzua

A decision procedure revisited: notes on direct logic, linear logic and its implementation

Gianluigi Bellin, Jussi Ketonen
1992 Theoretical Computer Science  
In addition, the implementation of a decision procedure for direct predicate logic is sketched.  ...  We will focus on the structure of direct predicate calculus as defined in Ketonen and Weyhrauch (1984) in the light of the recent work of Girard (Girard , 1988 ) on linear logic.  ...  In practice, irrelevance elimination significantly reduces the search space for valid paths: We may from now on assume that all literals in 9 are not irrelevant.  ... 
doi:10.1016/0304-3975(92)90069-r fatcat:zz4x4y4mobfchgtm6eskc5dygu

Optimization of Executable Formal Interpreters developed in Higher-order Theorem Proving Systems [article]

Zheng Yang, Hang Lei
2018 arXiv   pre-print
A specific FSPVM, denoted as FSPVM-E, was developed in Coq based on a general, extensible, and reusable formal memory (GERM) framework, an extensible and universal formal intermediate programming language  ...  , denoted as Lolisa, which is a large subset of the Solidity programming language that uses generalized algebraic datatypes, and a corresponding formally verified interpreter for Lolisa, denoted as FEther  ...  Moreover, the requirement that be simplified as the normal form eliminates irrelevant logic expressions from the computational load.  ... 
arXiv:1808.08511v1 fatcat:b3guwu4jhnaqpikwqm4cho7oj4

Event-Flow Graphs for Efficient Path-Sensitive Analyses [article]

Ahmed Tamrawi, Suresh Kothari
2015 arXiv   pre-print
The key challenge is how to efficiently compute equivalence classes of paths in a CFG without examining each path in the CFG?  ...  In this paper, we present a linear-time algorithm to form equivalence classes without the need for examination of each path in a CFG.  ...  irrelevant and will be eliminated by Algorithm II.  ... 
arXiv:1404.1279v3 fatcat:2thczov37zegffizmnydlcdsbe

Logic Programming with Focusing Proofs in Linear Logic

JEAN-MARC ANDREOLI
1992 Journal of Logic and Computation  
in the search are eliminated when aimed at focusing proofs) is identi ed.  ...  I propose here one such model, in the area of Logic Programming, where the basic computational principle is Computation = Proof search.  ...  Acknowledgement The material presented here is contained in a thesis of the university of Paris 6 by the author 3], which was prepared at the European Computer Industry Research Center (ECRC) in Munich  ... 
doi:10.1093/logcom/2.3.297 fatcat:xfbkveid4fcvfiaiyy7vdxqohm

ACL2s: "The ACL2 Sedan"

Peter C. Dillinger, Panagiotis Manolios, Daron Vroon, J. Strother Moore
2007 29th International Conference on Software Engineering (ICSE'07 Companion)  
It is the name of a programming language, a first-order mathematical logic based on recursive functions, and a mechanical theorem prover for that logic [9, 5, 4] .  ...  In general, the goal is to develop a tool that is "self-teaching," i.e., it should be possible for an undergraduate to sit down and play with it and learn how to program in ACL2 and how to reason about  ...  Acknowledgments We would like to thank Matt Kaufmann for help and guidance in hacking ACL2, Qiang Zhang for bug hunting, and Alexander Spiridonov for providing ACL2s support to students at the University  ... 
doi:10.1109/icsecompanion.2007.14 dblp:conf/icse/DillingerMVM07 fatcat:iklwsfqisrhj5edv2itk7biroa

ACL2s: "The ACL2 Sedan"

Peter C. Dillinger, Panagiotis Manolios, Daron Vroon, J. Strother Moore
2007 Electronical Notes in Theoretical Computer Science  
It is the name of a programming language, a first-order mathematical logic based on recursive functions, and a mechanical theorem prover for that logic [9, 5, 4] .  ...  In general, the goal is to develop a tool that is "self-teaching," i.e., it should be possible for an undergraduate to sit down and play with it and learn how to program in ACL2 and how to reason about  ...  Acknowledgments We would like to thank Matt Kaufmann for help and guidance in hacking ACL2, Qiang Zhang for bug hunting, and Alexander Spiridonov for providing ACL2s support to students at the University  ... 
doi:10.1016/j.entcs.2006.09.018 fatcat:lkkujngunjhffhze7nxvjhvsiq
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