Vladimir Lifschitz

Joohyung Lee, Vladimir Lifschitz, Ravi Palla

Safe first-order formulas generalize the concept of a safe rule, which plays an important role in the design of answer set solvers. We show that any safe sentence is equivalent, in a certain sense, to the result of its grounding -- to the variable-free sentence obtained from it by replacing all quantifiers with multiple conjunctions and disjunctions. It follows that a safe sentence and the result of its grounding have the same stable models, and that the stable models of a safe sentence can be characterized by a formula of a simple syntactic form.

Enrico Giunchiglia, Joohyung Lee, Vladimir Lifschitz et al.

This paper continues the line of work on representing properties of actions in nonmonotonic formalisms that stresses the distinction between being "true" and being "caused", as in the system of causal logic introduced by McCain and Turner and in the action language C proposed by Giunchiglia and Lifschitz. The only fluents directly representable in language C+ are truth-valued fluents, which is often inconvenient. We show that both causal logic and language C can be extended to allow values from arbitrary nonempty sets. Our extension of language C, called C+, also makes it possible to describe actions in terms of their attributes, which is important from the perspective of elaboration tolerance. We describe an embedding of C+ in causal theories with multi-valued constants, relate C+ to Pednault's action language ADL, and show how multi-valued constants can be eliminated in favor of Boolean constants.

Jorge Fandinno, Vladimir Lifschitz

Theory of stable models is the mathematical basis of answer set programming. Several results in that theory refer to the concept of the positive dependency graph of a logic program. We describe a modification of that concept and show that the new understanding of positive dependency makes it possible to strengthen some of these results. Under consideration in Theory and Practice of Logic Programming (TPLP).

Jorge Fandinno, Vladimir Lifschitz, Nathan Temple

Program completion is a translation from the language of logic programs into the language of first-order theories. Its original definition has been extended to programs that include integer arithmetic, accept input, and distinguish between output predicates and auxiliary predicates. For tight programs, that generalization of completion is known to match the stable model semantics, which is the basis of answer set programming. We show that the tightness condition in this theorem can be replaced by a less restrictive "local tightness" requirement. From this fact we conclude that the proof assistant anthem-p2p can be used to verify equivalence between locally tight programs. Under consideration for publication in Theory and Practice of Logic Programming

Jorge Fandinno, Vladimir Lifschitz

In answer set programming, two groups of rules are considered strongly equivalent if they have the same meaning in any context. Strong equivalence of two programs can be sometimes established by deriving rules of each program from rules of the other in an appropriate deductive system. This paper shows how to extend this method of proving strong equivalence to programs containing the counting aggregate.

Vinay K Chaudhri, Chaitan Baru, Brandon Bennett et al.

The long-standing goal of creating a comprehensive, multi-purpose knowledge resource, reminiscent of the 1984 Cyc project, still persists in AI. Despite the success of knowledge resources like WordNet, ConceptNet, Wolfram|Alpha and other commercial knowledge graphs, verifiable, general-purpose widely available sources of knowledge remain a critical deficiency in AI infrastructure. Large language models struggle due to knowledge gaps; robotic planning lacks necessary world knowledge; and the detection of factually false information relies heavily on human expertise. What kind of knowledge resource is most needed in AI today? How can modern technology shape its development and evaluation? A recent AAAI workshop gathered over 50 researchers to explore these questions. This paper synthesizes our findings and outlines a community-driven vision for a new knowledge infrastructure. In addition to leveraging contemporary advances in knowledge representation and reasoning, one promising idea is to build an open engineering framework to exploit knowledge modules effectively within the context of practical applications. Such a framework should include sets of conventions and social structures that are adopted by contributors.

Jorge Fandinno, Vladimir Lifschitz, Patrick Lühne et al.

This paper continues the line of research aimed at investigating the relationship between logic programs and first-order theories. We extend the definition of program completion to programs with input and output in a subset of the input language of the ASP grounder gringo, study the relationship between stable models and completion in this context, and describe preliminary experiments with the use of two software tools, anthem and vampire, for verifying the correctness of programs with input and output. Proofs of theorems are based on a lemma that relates the semantics of programs studied in this paper to stable models of first-order formulas. Under consideration for acceptance in TPLP.

Vladimir Lifschitz

This paper describes an approach to the methodology of answer set programming (ASP) that can facilitate the design of encodings that are easy to understand and provably correct. Under this approach, after appending a rule or a small group of rules to the emerging program we include a comment that states what has been "achieved" so far. This strategy allows us to set out our understanding of the design of the program by describing the roles of small parts of the program in a mathematically precise way.

Amelia Harrison, Vladimir Lifschitz

The definition of stable models for propositional formulas with infinite conjunctions and disjunctions can be used to describe the semantics of answer set programming languages. In this note, we enhance that definition by introducing a distinction between intensional and extensional atoms. The symmetric splitting theorem for first-order formulas is then extended to infinitary formulas and used to reason about infinitary definitions. This note is under consideration for publication in Theory and Practice of Logic Programming.

Amelia Harrison, Vladimir Lifschitz, Fangkai Yang

Input languages of answer set solvers are based on the mathematically simple concept of a stable model. But many useful constructs available in these languages, including local variables, conditional literals, and aggregates, cannot be easily explained in terms of stable models in the sense of the original definition of this concept and its straightforward generalizations. Manuals written by designers of answer set solvers usually explain such constructs using examples and informal comments that appeal to the user's intuition, without references to any precise semantics. We propose to approach the problem of defining the semantics of gringo programs by translating them into the language of infinitary propositional formulas. This semantics allows us to study equivalent transformations of gringo programs using natural deduction in infinitary propositional logic.

Vladimir Lifschitz, Fangkai Yang

We investigate the relationship between the generalization of program completion defined in 1984 by Lloyd and Topor and the generalization of the stable model semantics introduced recently by Ferraris et al. The main theorem can be used to characterize, in some cases, the general stable models of a logic program by a first-order formula. The proof uses Truszczynski's stable model semantics of infinitary propositional formulas.

Vladimir Lifschitz, Karl Pichotta, Fangkai Yang

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.