Reasoning with minimal models has always been at the core of many knowledge representation techniques, but we still have only a limited understanding of this problem in Description Logics (DLs). Minimization of some selected predicates, letting the remaining predicates vary or be fixed, as proposed in circumscription, has been explored and exhibits high complexity. The case of `pure' minimal models, where the extension of all predicates must be minimal, has remained largely uncharted. We address this problem in popular DLs and obtain surprisingly negative results: concept satisfiability in minimal models is undecidable already for $\mathcal{EL}$. This undecidability also extends to a very restricted fragment of tuple-generating dependencies. To regain decidability, we impose acyclicity conditions on the TBox that bring the worst-case complexity below double exponential time and allow us to establish a connection with the recently studied pointwise circumscription; we also derive results in data complexity. We conclude with a brief excursion to the DL-Lite family, where a positive result was known for DL-Lite$_{\text{core}}$, but our investigation establishes ExpSpace-hardness already for its extension DL-Lite$_{\text{horn}}$.

We study extensions of expressive decidable fragments of first-order logic with circumscription, in particular the two-variable fragment FO$^2$, its extension C$^2$ with counting quantifiers, and the guarded fragment GF. We prove that if only unary predicates are minimized (or fixed) during circumscription, then decidability of logical consequence is preserved. For FO$^2$ the complexity increases from $\textrm{coNexp}$ to $\textrm{coNExp}^\textrm{NP}$-complete, for GF it (remarkably!) increases from $\textrm{2Exp}$ to $\textrm{Tower}$-complete, and for C$^2$ the complexity remains open. We also consider querying circumscribed knowledge bases whose ontology is a GF sentence, showing that the problem is decidable for unions of conjunctive queries, $\textrm{Tower}$-complete in combined complexity, and elementary in data complexity. Already for atomic queries and ontologies that are sets of guarded existential rules, however, for every $k \geq 0$ there is an ontology and query that are $k$-$\textrm{Exp}$-hard in data complexity.

Circumscription is one of the main approaches for defining non-monotonic description logics (DLs). While the decidability and complexity of traditional reasoning tasks such as satisfiability of circumscribed DL knowledge bases (KBs) is well understood, for evaluating conjunctive queries (CQs) and unions thereof (UCQs), not even decidability had been established. In this paper, we prove decidability of (U)CQ evaluation on circumscribed DL KBs and obtain a rather complete picture of both the combined complexity and the data complexity, for DLs ranging from ALCHIO via EL to various versions of DL-Lite. We also study the much simpler atomic queries (AQs).

The pyglaf reasoner takes advantage of circumscription to solve computational problems of abstract argumentation frameworks. In fact, many of these problems are reduced to circumscription by means of linear encodings, and a few others are solved by means of a sequence of calls to an oracle for circumscription. Within pyglaf, Python is used to build the encodings and to control the execution of the external circumscription solver, which extends the SAT solver glucose and implements algorithms taking advantage of unsatisfiable core analysis and incremental computation.

Consistent answers to a query from a possibly inconsistent database are answers that are simultaneously retrieved from every possible repair of the database. Repairs are consistent instances that minimally differ from the original inconsistent instance. It has been shown before that database repairs can be specified as the stable models of a disjunctive logic program. In this paper we show how to use the repair programs to transform the problem of consistent query answering into a problem of reasoning w.r.t. a theory written in second-order predicate logic. It also investigated how a first-order theory can be obtained instead by applying second-order quantifier elimination techniques.

PIE is a Prolog-embedded environment for automated reasoning on the basis of first-order logic. Its main focus is on formulas, as constituents of complex formalizations that are structured through formula macros, and as outputs of reasoning tasks such as second-order quantifier elimination and Craig interpolation. It supports a workflow based on documents that intersperse macro definitions, invocations of reasoners, and LaTeX-formatted natural language text. Starting from various examples, the paper discusses features and application possibilities of PIE along with current limitations and issues for future research.

PIE is a Prolog-embedded environment for automated reasoning on the basis of first-order logic. It includes a versatile formula macro system and supports the creation of documents that intersperse macro definitions, reasoner invocations and LaTeX-formatted natural language text. Invocation of various reasoners is supported: External provers as well as sub-systems of PIE, which include preprocessors, a Prolog-based first-order prover, methods for Craig interpolation and methods for second-order quantifier elimination.

One of the major problems in developing so-called intelligent computer-aided design (CAD) systems (ten Hagen and Tomiyama 1987) is the representation of design knowledge, which is a two-part process: the representation of design objects and the representation of design processes. We believe that intelligent CAD systems will be fully realized only when these two types of representation are integrated. Progress has been made in the representation of design objects, as can be seen, for example, in geometric modeling; however, almost no significant results have been seen in the representation of design processes, which implies that we need a design theory to formalize them. According to Finger and Dixon (1989), design process models can be categorized into a descriptive model that explains how design is done, a cognitive model that explains the designer's behavior, a prescriptive model that shows how design must be done, and a computable model that expresses a method by which a computer can accomplish a task. A design theory for intelligent CAD is not useful when it is merely descriptive or cognitive; it must also be computable.

John McCarthy's contributions to computer science and artificial intelligence are legendary. He invented Lisp, made substantial contributions to early work in timesharing and the theory of computation, and was one of the founders of artificial intelligence and knowledge representation. This article, written in honor of McCarthy's 80th birthday, presents a brief biography, an overview of the major themes of his research, and a discussion of several of his major papers. It was not his dream of an intelligent computer that was unique, or even first: Alan Turing (Turing 1950) had envisioned a computer that could converse intelligently with humans back in 1950; by the mid 1950s, there were several researchers (including Herbert Simon, Allen Newell, Oliver Selfridge, and Marvin Minsky) working in what would be called artificial intelligence. What distinguished McCarthy's plan was his emphasis on using mathematical logic both as a language for representing the knowledge that an intelligent machine should have and as a means for reasoning with that knowledge.

THE UNIVERSITY OF MARYLAND'S Computer Science Department conducts a broad research program in both theoretical and applied artificial intelligence. Nine faculty and more than fifty research associates and graduate students are involved in AI research. Projects are funded by a large number of government agencies, as well as by several major corporations. The computing environment will improve dramatically over the next several years, due in large part to a Coordinated Experimental Research Equipment Grant awarded to the Computer Science Department by the National Science Foundation in 1982. In addition to the research program in AI, the Department offers a large number of courses at both the graduate and undergraduate levels on all facets of AI.