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

2021
*
arXiv
*
pre-print

The

arXiv:2105.14100v1
fatcat:gnimp7ycsjderb7exdikoh6kwa
*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*". ...##
###
Latticed k-Induction with an Application to Probabilistic Programs
[chapter]

2021
*
Lecture Notes in Computer Science
*

us

doi:10.1007/978-3-030-81688-9_25
fatcat:7pgsk7tlcrfv7nn7rmjkbsaviu
*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 ...##
###
Latticed $k$-Induction with an Application to Probabilistic Programs

2021

The

doi:10.18154/rwth-2021-06838
fatcat:crgow7jbazbjxprdh3rsypexiy
*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 ...##
###
Termination of logic programs with imperfect information: applications and query procedure

2007
*
Journal of Applied Logic
*

We apply the termination results

doi:10.1016/j.jal.2006.03.004
fatcat:7c2v6kd6ijcbtb7ayeuhprz3a4
*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. ...##
###
Hybrid Probabilistic Logic Programs as Residuated Logic Programs
[chapter]

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. ...

##
###
Knowledge compilation of logic programs using approximation fixpoint theory

2015
*
Theory and Practice of Logic Programming
*

In this paper, we show how

doi:10.1017/s1471068415000162
fatcat:o7mzezlgonetrck7rncv3cys54
*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 . ...##
###
The Distribution Semantics is Well-Defined for All Normal Programs

2015
*
International Conference on Logic Programming
*

In this paper we show that it is possible

dblp:conf/iclp/Riguzzi15
fatcat:rcvs76djtraz3hapamebnpxbny
*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. ...##
###
Formalising Semantics for Expected Running Time of Probabilistic Programs
[chapter]

2016
*
Lecture Notes in Computer Science
*

We want

doi:10.1007/978-3-319-43144-4_30
fatcat:ldcfxkpvrbapvpyma4p2berdvm
*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*...##
###
Sorted Multi-adjoint Logic Programs: Termination Results and Applications
[chapter]

2004
*
Lecture Notes in Computer Science
*

Several extensions of these conditions are presented and related

doi:10.1007/978-3-540-30227-8_23
fatcat:ogcqfm2o6jgitjbuvmmdkphkhq
*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 ...##
###
A Tabulation Proof Procedure for First-order Residuated Logic Programs: Soundness, Completeness and Optimizations

2006
*
2006 IEEE International Conference on Fuzzy Systems
*

Residuated logic

doi:10.1109/fuzzy.2006.1681978
dblp:conf/fuzzIEEE/DamasioMO06
fatcat:7ufd6tdtgzgo3ej4quximvix6m
*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 ...##
###
Book announcements

1984
*
Discrete Applied Mathematics
*

Dufresne:

doi:10.1016/0166-218x(84)90070-2
fatcat:75txrigmzzaw5ef5itdxwfbdea
*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. ...##
###
Probabilistic construction of deterministic algorithms: Approximating packing integer programs

1988
*
Journal of computer and system sciences (Print)
*

For several packing problems, we prove

doi:10.1016/0022-0000(88)90003-7
fatcat:y3meejfmsrevhn64wfghkisqse
*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*,. ...##
###
Probabilistic logic programming

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*. ...

##
###
Recovering Noisy Contexts with Probabilistic Formal Concepts

2016
*
International Conference on Concept Lattices and their Applications
*

due

dblp:conf/cla/Martynovich16
fatcat:p4r3ze5jf5b25fjfmujb4ahxim
*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. ...##
###
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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