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Latticed k-Induction with an Application to Probabilistic Programs [article]

Kevin Batz, Mingshuai Chen, Benjamin Lucien Kaminski, Joost-Pieter Katoen, Christoph Matheja, Philipp Schröer
2021 arXiv   pre-print
The lattice-theoretic understanding of k-induction and BMC enables us to apply both techniques to the fully automatic verification of infinite-state probabilistic programs.  ...  maps on complete lattices, and (iii) extends from naturals k to transfinite ordinals κ, thus yielding κ-induction.  ...  Benjamin Lucien Kaminski is indebted to Larry Fischer for his linguistic advice-this time on the word "latticed".  ... 
arXiv:2105.14100v1 fatcat:gnimp7ycsjderb7exdikoh6kwa

Latticed k-Induction with an Application to Probabilistic Programs [chapter]

Kevin Batz, Mingshuai Chen, Benjamin Lucien Kaminski, Joost-Pieter Katoen, Christoph Matheja, Philipp Schröer
2021 Lecture Notes in Computer Science  
us to apply both techniques to the fully automatic verification of infinite-state probabilistic programs.  ...  maps on complete lattices, and (iii) extends from naturals k to transfinite ordinals $$\kappa $$ κ , thus yielding $$\kappa $$ κ -induction.The lattice-theoretic understanding of k-induction and BMC enables  ...  Probabilistic Programs In the remainder of this article, we employ latticed k-induction and BMC to verify imperative programs with access to discrete probabilistic choices-branching on the outcomes of  ... 
doi:10.1007/978-3-030-81688-9_25 fatcat:7pgsk7tlcrfv7nn7rmjkbsaviu

Latticed $k$-Induction with an Application to Probabilistic Programs

Kevin Batz, Mingshuai Chen, Benjamin Lucien Kaminski, Joost-Pieter Katoen, Christoph Matheja, Philipp Schröer
2021
The lattice-theoretic understanding of k-induction and BMC enables us to apply both techniques to the fully automatic verification of infinitestate probabilistic programs.  ...  maps on complete lattices, and (iii) extends from naturals k to transfinite ordinals κ, thus yielding κ-induction.  ...  Probabilistic Programs In the remainder of this article, we employ latticed k-induction and BMC to verify imperative programs with access to discrete probabilistic choices-branching on the outcomes of  ... 
doi:10.18154/rwth-2021-06838 fatcat:crgow7jbazbjxprdh3rsypexiy

Termination of logic programs with imperfect information: applications and query procedure

C.V. Damásio, J. Medina, M. Ojeda-Aciego
2007 Journal of Applied Logic  
We apply the termination results to probabilistic and fuzzy logic programming languages, enabling the use of the tabulation proof procedure for query answering.  ...  A general logic programming framework allowing for the combination of several adjoint lattices of truth-values is presented.  ...  Our induction hypothesis will be that there exists an integer k such that r j T k P (C j ) for all roots C j : r j in a forest generated in n steps.  ... 
doi:10.1016/j.jal.2006.03.004 fatcat:7c2v6kd6ijcbtb7ayeuhprz3a4

Hybrid Probabilistic Logic Programs as Residuated Logic Programs [chapter]

Carlos Viegas Damásio, Luís Moniz Pereira
2000 Lecture Notes in Computer Science  
Programming, Hybrid Probabilistic Logic Programs, and Possibilistic Logic Programming.  ...  In this paper we show the embedding of Hybrid Probabilistic Logic Programs into the rather general framework of Residuated Logic Programs, where the main results of (de nite) logic programming are validly  ...  Thus, when evaluating F s 1 F 1 u : : : u s k F k with respect to interpretation I we really mean I(F) s 1 I(F 1 ) u : : : u s k I(F k ) , as usual.  ... 
doi:10.1007/3-540-40006-0_5 fatcat:ypzpla3kjrg2dmrjjnxrea7ole

Knowledge compilation of logic programs using approximation fixpoint theory

BART BOGAERTS, GUY VAN DEN BROECK
2015 Theory and Practice of Logic Programming  
In this paper, we show how to extend it to general logic programs under the well-founded semantics.We develop our work in approximation fixpoint theory, an algebraical framework that unifies semantics  ...  As such, our algebraical results are also applicable to autoepistemic logic, default logic and abstract dialectical frameworks.  ...  If f : L → K is a lattice morphism, f 2 : L 2 → K 2 : (x, y) → (f (x), f (y)) is a lattice morphism from the bilattice L 2 to the bilattice K 2 .  ... 
doi:10.1017/s1471068415000162 fatcat:o7mzezlgonetrck7rncv3cys54

The Distribution Semantics is Well-Defined for All Normal Programs

Fabrizio Riguzzi
2015 International Conference on Logic Programming  
In this paper we show that it is possible to define the semantics for all programs.  ...  The distribution semantics is an approach for integrating logic programming and probability theory that underlies many languages and has been successfully applied in many domains.  ...  Lemma 12 For a ground probabilistic logic program P with probabilistic facts F, rules R and atoms B P , let K α a and K α ¬a be the formulas associated with atom a in IFPC P ↑ α.  ... 
dblp:conf/iclp/Riguzzi15 fatcat:rcvs76djtraz3hapamebnpxbny

Formalising Semantics for Expected Running Time of Probabilistic Programs [chapter]

Johannes Hölzl
2016 Lecture Notes in Computer Science  
We want to use this work to implement a program logic in Isabelle/HOL to verify the expected running time of pGCL programs. We base it on recent work by Kaminski, Katoen, Matheja, and Olmedo.  ...  The second semantics interprets a pGCL program in terms of a Markov decision process (MDPs), i.e. it provides an operational semantics. Finally we show the equivalence of both running time semantics.  ...  They present semantics and proof rules to analyse the expected running time of probabilistic guarded command language (pGCL) programs. pGCL is an interesting programming language as it admits probabilistic  ... 
doi:10.1007/978-3-319-43144-4_30 fatcat:ldcfxkpvrbapvpyma4p2berdvm

Sorted Multi-adjoint Logic Programs: Termination Results and Applications [chapter]

C. V. Damásio, J. Medina, M. Ojeda-Aciego
2004 Lecture Notes in Computer Science  
Several extensions of these conditions are presented and related to some well-known formalisms for probabilistic logic programming.  ...  A general framework of logic programming allowing for the combination of several adjoint lattices of truth-values is presented.  ...  Each A s is a nonempty set called the carrier of sort s, 2. and I is a function which assigns a map I(f ) : A s1 × · · · × A s k → A s to each f : s 1 × · · · × s k → s ∈ F , where k > 0, and an element  ... 
doi:10.1007/978-3-540-30227-8_23 fatcat:ogcqfm2o6jgitjbuvmmdkphkhq

A Tabulation Proof Procedure for First-order Residuated Logic Programs: Soundness, Completeness and Optimizations

C.V. Damasio, J. Medina, M. Ojeda-Aciego
2006 2006 IEEE International Conference on Fuzzy Systems  
Residuated logic programs have shown to be a generalisation of a number of approaches to logic programming under uncertain or vague information, including fuzzy or annotated or probabilistic or similarity-based  ...  logic programming frameworks.  ...  By application of induction hypothesis, we have that T P ↑ n (B k ζ) ≤ r(B k ζ) and there is an answer in B k σ with computed value r(B k ζ) (we will denote it s k for brevity) which unifies with B k ζ  ... 
doi:10.1109/fuzzy.2006.1681978 dblp:conf/fuzzIEEE/DamasioMO06 fatcat:7ufd6tdtgzgo3ej4quximvix6m

Book announcements

1984 Discrete Applied Mathematics  
Dufresne: An application of MACSYMA to nonlinear systems decoupling. A.J. KFOURY, Robert N. MOLL and Michael A. ARBIB, A Programming Approach to Computability, Texts and Monographs Preface.  ...  Kozen: A programming language for the inductive sets, and applications. K.A. Kalorkoti: A lower bound for the formula size of rational functions. J.  ... 
doi:10.1016/0166-218x(84)90070-2 fatcat:75txrigmzzaw5ef5itdxwfbdea

Probabilistic construction of deterministic algorithms: Approximating packing integer programs

Prabhakar Raghavan
1988 Journal of computer and system sciences (Print)  
For several packing problems, we prove probabilistically that there exists an integer solution close to the optimum of the relaxation solution.  ...  In each case we compute the relaxation optimum and use this information to develop an approximation algorithm for the integer program. In Section 1 we introduce the lattice approximation problem.  ...  This can be formulated as an integer program as follows. We use an indicator (0 -1) variable xi to indicate whether or not the vector Vi is selected to represent lj; here 1 <j < r and 1 <k < k,.  ... 
doi:10.1016/0022-0000(88)90003-7 fatcat:y3meejfmsrevhn64wfghkisqse

Probabilistic logic programming

Raymond Ng, V.S. Subrahmanian
1992 Information and Computation  
To our knowledge, this is the tirst probabilistic characterization of logic programming semantics. Ii 1  ...  A probabilistic model theory and lixpoint theory is developed for such programs. This probabilistic model theory satisfies the requirements proposed by ) for a function to be called probabilistic.  ...  The frameworks of Blair and Subrahmanian (1988) have dealt with lattice-based logic programming.  ... 
doi:10.1016/0890-5401(92)90061-j fatcat:7libj2wupbf5jpxmgqjr7aan3i

Recovering Noisy Contexts with Probabilistic Formal Concepts

Vitaliy V. Martynovich, Euvgeniy E. Vityaev
2016 International Conference on Concept Lattices and their Applications  
due to an overfitting.  ...  The uncertainty in the environment typically generates noisy concept alternatives and leads to an overpopulated concept lattice.  ...  According to the method discussed in Section 7, a computer program was implemented to perform a semantical probabilistic inference.  ... 
dblp:conf/cla/Martynovich16 fatcat:p4r3ze5jf5b25fjfmujb4ahxim

Page 1988 of Mathematical Reviews Vol. , Issue 90M [page]

1990 Mathematical Reviews  
90m:0 3044 90m:03044 03B48 03405 Howson, Colin (4-LSE) Discussion: on a recent objection to Popper and Miller’s “disproof” of probabilistic induction: “Dualling: a critique of an argument of Popper and  ...  On an intuitionistic lattice L, a relational probability is defined as a mapping from L x L into [0,1] such that (1) p(a’/k) =1- p(a/k) and (2) p(ab/k) = p(a/k)p(b/k).  ... 
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