Related papers: Extremal problems in logic programming and stable …
We introduce the task of algorithm class prediction for programming word problems. A programming word problem is a problem written in natural language, which can be solved using an algorithm or a program. We define classes of various…
Non deterministic applications arise in many domains, including, stochastic optimization, multi-objectives optimization, stochastic planning, contingent stochastic planning, reinforcement learning, reinforcement learning in partially…
In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications. These justifications are expressed in terms of causal graphs…
The integration of reasoning, learning, and decision-making is key to build more general artificial intelligence systems. As a step in this direction, we propose a novel neural-logic architecture, called differentiable logic machine (DLM),…
This paper presents the first study of the complexity of the optimization problem for integer linear-exponential programs which extend classical integer linear programs with the exponential function $x \mapsto 2^x$ and the remainder…
Program correctness (in imperative and functional programming) splits in logic programming into correctness and completeness. Completeness means that a program produces all the answers required by its specification. Little work has been…
Logic Programs with Ordered Disjunction (LPODs) extend classical logic programs with the capability of expressing alternatives with decreasing degrees of preference in the heads of program rules. Despite the fact that the operational…
In this paper we apply computer-aided theorem discovery technique to discover theorems about strongly equivalent logic programs under the answer set semantics. Our discovered theorems capture new classes of strongly equivalent logic…
A long-standing open question in Integer Programming is whether integer programs with constraint matrices with bounded subdeterminants are efficiently solvable. An important special case thereof are congruency-constrained integer programs…
One of the long-standing research problems on logic programming is to treat the cut predicate in a logical, high-level way. We argue that this problem can be solved by adopting linear logic and choice-disjunctive goal formulas of the form…
This paper introduces a fundamental result, which is relevant for Answer Set programming, and planning. For the first time since the definition of the stable model semantics, the class of logic programs for which a stable model exists is…
We establish the expressibility in fixed-point logic with counting (FPC) of a number of natural polynomial-time problems. In particular, we show that the size of a maximum matching in a graph is definable in FPC. This settles an open…
We settle the computational complexity of fundamental questions related to multicriteria integer linear programs, when the dimensions of the strategy space and of the outcome space are considered fixed constants. In particular we construct:…
We study the problem of finding solutions to the stable matching problem that are robust to errors in the input and we obtain a polynomial time algorithm for a special class of errors. In the process, we also initiate work on a new…
Many researchers in artificial intelligence are beginning to explore the use of soft constraints to express a set of (possibly conflicting) problem requirements. A soft constraint is a function defined on a collection of variables which…
In this paper we generalize N-fold integer programs and two-stage integer programs with N scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N, these integer programs are polynomial-time…
Disjunctive Answer Set Programming is a powerful declarative programming paradigm with complexity beyond NP. Identifying classes of programs for which the consistency problem is in NP is of interest from the theoretical standpoint and can…
The regular models of a normal logic program are a particular type of partial (i.e. 3-valued) models which correspond to stable partial models with minimal undefinedness. In this paper, we explore graphical conditions on the dependency…
We consider the question of determining whether or not a given system of fractional-order differential equations is (asymptotically) stable. In particular, we admit systems where each constituent equation may have its own order, independent…
The goal of inductive logic programming is to induce a logic program (a set of logical rules) that generalises training examples. Inducing programs with many rules and literals is a major challenge. To tackle this challenge, we introduce an…