Lifschitz, Vladimir


Answer Sets and the Language of Answer Set Programming

AI Magazine

Answer set programming is a declarative programming paradigm based on the answer set semantics of logic programs. This introductory article provides the mathematical background for the discussion of answer set programming in other contributions to this special issue.


Answer Sets and the Language of Answer Set Programming

AI Magazine

Answer set programming is a declarative programming paradigm based on the answer set semantics of logic programs. This introductory article provides the mathematical background for the discussion of answer set programming in other contributions to this special issue.


The Winograd Schema Challenge and Reasoning about Correlation

AAAI Conferences

The Winograd Schema Challenge is an alternative to the Turing Test that may provide a more meaningful measure of machine intelligence. It poses a set of coreference resolution problems that cannot be solved without human-like reasoning. In this paper, we take the view that the solution to such problems lies in establishing discourse coherence. Specifically, we examine two types of rhetorical relations that can be used to establish discourse coherence: positive and negative correlation. We introduce a framework for reasoning about correlation between sentences, and show how this framework can be used to justify solutions to some Winograd Schema problems.


Pearl's Causality in a Logical Setting

AAAI Conferences

We provide a logical representation of Pearl's structural causal models in the causal calculus of McCain and Turner (1997) and its first-order generalization by Lifschitz. It will be shown that, under this representation, the nonmonotonic semantics of the causal calculus describes precisely the solutions of the structural equations (the causal worlds of the causal model), while the causal logic from Bochman (2004) is adequate for describing the behavior of causal models under interventions (forming submodels).


Relational Theories with Null Values and Non-Herbrand Stable Models

arXiv.org Artificial Intelligence

Generalized relational theories with null values in the sense of Reiter are first-order theories that provide a semantics for relational databases with incomplete information. In this paper we show that any such theory can be turned into an equivalent logic program, so that models of the theory can be generated using computational methods of answer set programming. As a step towards this goal, we develop a general method for calculating stable models under the domain closure assumption but without the unique name assumption.


Logic Programs with Intensional Functions

AAAI Conferences

The stable model semantics treats a logic program as a mechanism for specifying its intensional predicates. In this paper we discuss a modification of that semantics in which functions, rather than predicates, are intensional. The idea of the new definition comes from nonmonotonic causal logic.



Representing First-Order Causal Theories by Logic Programs

arXiv.org Artificial Intelligence

Nonmonotonic causal logic, introduced by Norman McCain and Hudson Turner, became a basis for the semantics of several expressive action languages. McCain's embedding of definite propositional causal theories into logic programming paved the way to the use of answer set solvers for answering queries about actions described in such languages. In this paper we extend this embedding to nondefinite theories and to first-order causal logic.


Symmetric Splitting in the General Theory of Stable Models

AAAI Conferences

Splitting a logic program allows us to reduce the task of computing its stable models to similar tasks for smaller programs.  This idea is extended here to the general theory of stable models that replaces traditional logic programs by arbitrary first-order sentences and distinguishes between intensional and extensional predicates.  We discuss two kinds of splitting: a set of intensional predicates can be split into subsets, and a formula can be split into its conjunctive terms.


The Sixth International Workshop on Nonmonotonic Reasoning

AI Magazine

The Sixth International Workshop on Nonmonotonic Reasoning was held 10 to 12 June 1996 in Timberline, Oregon. The aim of the workshop was to bring together active researchers interested in nonmonotonic reasoning to discuss current research, results, and problems of both a theoretical and a practical nature.