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Latticed k-Induction with an Application to Probabilistic Programs
[article]
2021
arXiv
pre-print
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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]
2021
Lecture Notes in Computer Science
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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
2021
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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
2007
Journal of Applied Logic
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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]
2000
Lecture Notes in Computer Science
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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
2015
Theory and Practice of Logic Programming
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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
2015
International Conference on Logic Programming
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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]
2016
Lecture Notes in Computer Science
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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]
2004
Lecture Notes in Computer Science
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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
2006
2006 IEEE International Conference on Fuzzy Systems
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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
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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
1988
Journal of computer and system sciences (Print)
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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
1992
Information and Computation
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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
2016
International Conference on Concept Lattices and their Applications
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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
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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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