L. Thorne McCarty

Explanation-Based Generalization as Resolution Theorem Proving

This paper presents Explanation-Based Generalization as an augmentation of resolution theorem proving for Horn Clause Logic. The corresponding implementation, PROLOG-EBG, performs generalization as a byproduct of standard PROLOG theorem proving. This results in very a concise (four-clause) implementation of EBG. The propagation of consistent variable bindings by PROLOG during theorem proving corrects an error in the previously published EBG algorithm.

Clausal intuitionistic logic I. Fixed-point semantics

Abstract Since the advent of Horn-clause logic programming in the mid 1970s, there have been numerous attempts to extend the expressive power of Horn-clause logic while preserving some of its attractive computational properties. This article, the first of a pair, presents a clausal language that extends Horn-clause logic by adding negations and embedded implications to the righthand side of a rule, and interpreting these new rules intuitionistically, in a set of partial models. The resulting system is shown to have a fixed-point semantics that generalizes the van Emden-Kowalski semantics for Horn clauses.

An implementation of Eisner v. Macomber

Eisner v. Macomber , 252 U.S. 189 (1920), a corporate tax case, was the principal illustration of a theory of legal reasoning and legal argumentation proposed more than ten years ago. Although the theory was described in some detail, using the vocabulary of prototypes and deformations, it was never fully implemented. There were two main problems: (1) the knowledge represen- tation languages available at the time were not suf- ciently expressive, and (2) as a result, the central concept of a prototype was never suciently formal- ized. These problems have been remedied by subse- quent work, and the present paper describes an im- plementation (in PROLOG) of the original theory. A study of the implemented system provides a rational reconstruction of the arguments of Justice Pitney and Justice Brandeis in this seminal corporate tax case.

Deep semantic interpretations of legal texts

One of the main obstacles to progress in the field of artificial intelligence and law is the natural language barrier, but the technology of natural language processing has advanced recently. In this paper, we will show that a state-of-the-art statistical parser can handle even the complex syntactic constructions of an appellate court judge, and that a deep semantic interpretation of the full text of a judicial opinion can be computed automatically from the output of the parser. Our ultimate goal is to use this semantic interpretation to extract from a judicial opinion precisely the information that a lawyer wants to know about a case.

Defeasible Deontic Reasoning

This paper combines a system of deontic logic with a system for default reasoning to analyze a notorious philosophical problem: Chisholms Paradox. The basic approach is to write deontic rules with explicit exceptions, but we also consider the extent to which a set of implicit exceptions can be derived from the underlying deontic semantics.

Some arguments about legal arguments

Everyone knows that lawyers are trained in the art of argument. But what exactly does this mean? Is a legal argument a chain of valid inferences, grounded in authoritative rules? Or is it merely a chain of plausible inferences? Does it require the citation of cases, pro and con? Are there canons of correct, or acceptable, argumentation? Can lawyers agree about what counts as a persuasive argument in a particular case, even if they disagree about the correct outome? These are important questions, and the literature in AI and Law has exploded recently with books and articles that purport to answer them. The titles alone are revealing: Modeling Legal Argument: Reasoning with Cases and Hypotheticals [Ashley, 1990]; Arguments and Cases: An Inevitable Intertwining [Skalak and Rissland, 1992]; Logical Tools for Modeling Legal Argument [Prakken, 1993]; A Formal Model of Legal Argumentation [Sartor, 1994]; The Pleadings Game: An Exercise in Computational Dialectics [Gordon, 1994]; A Dialectical Model of Assessing Conflicting Arguments in Legal Reasoning [Prakken and Sartor, 1996a]. It would appear from these examples that “argument” is the centerpiece of our subject. In this paper, I will argue (and the self reference is intentional) that most of this work is misleading, and misrepresents the true nature of legal argument. I will set the stage in Section 2 by reviewing the rudiments of civil procedure in the United States, and describing the contexts in which legal arguments occur. Sections 3 and 4, which follow, are the main critical sections of the paper. Section 3 discusses “rule-based” theories of legal argument, as represented by Gordon, Prakken and Sartor. Section 4 discusses “case-based” theories of legal argument, as represented by Rissland, Ashley and Skalak. Section 5 then discusses my own theory briefly. In the polemical spirit in which this paper is offered, I call this simply “The Correct Theory”. Throughout the discussion, I will assume that our main goal is theoretical, not practical. That is, I will assume that we are trying to acquire an understanding

Ownership: A case study in the representation of legal concepts

This article is an exercise in computational jurisprudence. It seems clear thatthe field of AI and Law should draw upon the insights of legal philosophers,whenever possible. But can the computational perspective offer anything inreturn? I will explore this question by focusing on the concept of OWNERSHIP,which has been debated in the jurisprudential literature for centuries. Althoughthe intellectual currents here flow mostly in one direction – from legal philosophy to AI – I will show that there are also some insights to be gained from a computational analysis of the OWNERSHIP relation. In particular, the article suggests a computational explanation for the emergence of abstract property rights, divorced from concrete material objects.

Modalities over actions, I. model theory

Abstract This paper analyzes a language for actions and the deontic modalities over actions — i.e., the modalities permitted, forbidden and obligatory . The work is based on: (1) an action language that allows the representation of concurrent and repetitive events; (2) a deontic language that allows the representation of “free choice permissions”; (3) a proof procedure that admits a logic programming style of computation; and (4) a facility for nonmonotonic inference based on negation-as-failure. Applications of the language to several problems of common sense reasoning are also discussed. In particular, by imposing a “causal assumption” on the deontic modalities, we obtain an interesting solution to the frame problem and the ramification problem. This first part of the paper includes a model theory, and a sequel will include a proof theory, with soundness and completeness results for various fragments of the language.

On the role of prototypes in appellate legal argument (abstract)

Although most of the work on Artificial Intelligence and Law today is oriented towards the development of pract ical systems, there is a small group of researchers who are primarily interested in theoretical questions: How much of legal reasoning can be reduced to reasoning wit h rules? Is this rule-based component significant, or trivial? How is it possible to rewon with cases at all? Are legal concepts just like ordinary common sense concepts, or do they have special characteristics? Is it possible to develop a computational theory of legal argument? The researchers who have investigated these questions include: Anne Gardner [1 I]; Edwina Rissland and her students, Kevin Ashley [38, 1] and David Skalak [39, 41]; Michael Dyer and his student, Seth Goldman [12]; Karl Branting [5]; and Keith Bellairs [2], In addition, researchers such as Richard Susskind [45] and J .C. Smith [43], who have primarily built practical systems, have also been deeply concerned with the jurisprudential foundations of the field.

Circumscribing embedded implications (without stratifications)

D This paper is a study of circumscription, not in classical logic, as usual, but in intuitionistic logic. We first review the intuitionistic circumscription of Horn clause logic programs, which was discussed in previous work, and we then consider the larger class of embedded implications. The ordinary circumscription axiom turns out to be inappropriate for this class of rules, and we analyze two alternatives: (1) prioritized circumscription, which works for stratified embedded implications; (2) partial circumscription, which is independent of the stratification. We then show that these two approaches coincide by identifying a single structure that serves as the jinal Krpke model for both circumscription axioms. This means that prioritized circumscription and partial circumscription entail exactly the same set of implicational queries. Several applications of these ideas are described, including (1) an interpretation of negation-as-failure, (2) a formalization of indefinite reasoning with definite rules, and (3) a methodology for analyzing inductive properties of PROLOG programs. a McCarthy’s theory of circumscription [33, 341 has been thoroughly investigated for a number of years, but it appears that all of these investigations have been conducted within the framework of classical logic. In this paper, we take a different approach: We analyze the circumscription axiom as a sentence in second-order intuitionistic logic, and we apply it to a class of formulae called embedded implications. We show that this variant of circumscription has interesting properties and potentially useful applications.