A dialectical model of assessing conflicting arguments in legal reasoning

Inspired by legal reasoning, this paper presents a formal framework for assessing conflicting arguments. Its use is illustrated with applications to realistic legal examples, and the potential for implementation is discussed. The framework has the form of a logical system for defeasible argumentation. Its language, which is of a logic-programming-like nature, has both weak and explicit negation, and conflicts between arguments are decided with the help of priorities on the rules. An important feature of the system is that these priorities are not fixed, but are themselves defeasibly derived as conclusions within the system. Thus debates on the choice between conflicting arguments can also be modelled.The proof theory of the system is stated in dialectical style, where a proof takes the form of a dialogue between a proponent and an opponent of an argument. An argument is shown to be justified if the proponent can make the opponent run out of moves in whatever way the opponent attacks. Despite this dialectical form, the system reflects a declarative, or relational approach to modelling legal argument. A basic assumption of this paper is that this approach complements two other lines of research in AI and Law, investigations of precedent-based reasoning and the development of procedural, or dialectical models of legal argument.Supported by a research fellowship of the Royal Netherlands Academy of Arts and Sciences, and by Esprit WG 8319 Modelage.     

Human-oriented and machine-oriented reasoning: Remarks on some problems in the history of Automated Theorem Proving

Examples in the history of Automated Theorem Proving are given, in order to show that even a seemingly mechanical activity, such as deductive inference drawing, involves special cultural features and tacit knowledge. Mechanisation of reasoning is thus regarded as a complex undertaking in cultural pruning of human-oriented reasoning. Sociological counterparts of this passage from human- to machine-oriented reasoning are discussed, by focusing on problems of man-machine interaction in the area of computer-assisted proof processing.     

Validating the PSL/Sugar Semantics Using Automated Reasoning

The Accellera organisation selected Sugar, IBMs formal specification language, as the basis for a standard to drive assertion-based verification in the electronics industry. Sugar combines regular expressions, Linear Temporal Logic (LTL) and Computation Tree Logic (CTL) into a property language intended for both static verification (e.g. model checking) and dynamic verification (e.g. simulation). In 2003 Accellera decided to rename the evolving standard to Accellera Property Specification Language (or PSL for short). We motivate and describe a deep semantic embedding of PSL in the version of higher-order logic supported by the HOL 4 theorem-proving system. The main goal of this paper is to demonstrate that mechanised theorem proving can be a useful aid to the validation of the semantics of an industrial design language.     

The liberalized δ-rule in free variable semantic tableaux

In this paper we have a closer look at one of the rules of the tableau calculus presented by Fitting [4], called the -rule. We prove that a modification of this rule, called the ⁺-rule, which uses fewer free variables, is also sound and complete. We examine the relationship between the ⁺-rule and variations of the -rule presented by Smullyan [9]. This leads to a second proof of the soundness of the ⁺-rule. An example shows the relevance of this modification for building tableau-based theorem provers.     

Predicate logic with flexibly binding operators and natural language semantics

A new formalism for predicate logic is introduced, with a non-standard method of binding variables, which allows a compositional formalization of certain anaphoric constructions, including donkey sentences and cross-sentential anaphora. A proof system in natural deduction format is provided, and the formalism is compared with other accounts of this type of anaphora, in particular Dynamic Predicate Logic.Both authors have been supported by grants from the Swedish Council for Research in the Humanities and Social Sciences.     

A New Implementation of Automath

This paper presents aut, a modern Automath checker. It is a straightforward re-implementation of the Zandleven Automath checker from the seventies. It was implemented about five years ago, in the programming language C. It accepts both the AUT-68 and AUT-QE dialects of Automath. This program was written to restore a damaged version of Jutting's translation of Landau's Grundlagen. Some notable features: It is fast. On a 1 GHz machine it will check the full Jutting formalization (736 K of nonwhitespace Automath source) in 0.6 seconds. Its implementation of -terms does not use named variables or de Bruijn indices (the two common approaches) but instead uses a graph representation. In this representation variables are represented by pointers to a binder. The program can compile an Automath text into one big Automath single line-style -term. It outputs such a term using de Bruijn indices. (These -terms cannot be checked by modern systems like Coq or Agda, because the -typed -calculi of de Bruijn are different from the -typed -calculi of modern type theory.)The source of aut is freely available on the Web at the address .     

Model-based cognitive diagnosis

This paper considers the problem of cognitive diagnosis as an instance of general diagnosis, as studied in artificial intelligence. Cognitive diagnosis is the process of inferring a cognitive state from observations of performance. It is thus a key component of any system which attempts to build a dynamic model of the user of that system. Many issues in cognitive diagnosis, previously discussed informally, are mapped onto formal techniques, with consequent increased clarity and rigour. But it is concluded that the general theories for diagnosis must be broadened to fully encompass the problems of cognitive diagnosis.     

ε-Entropy and Fractal Dimension of a State for a Gaussian Measure

Kolmogorov introduced the concept of -entropy to analyze information in classical continuous systems. The fractal dimension of a geometric set was introduced by Mandelbrot as a new criterion to analyze the geometric complexity of the set. The -entropy and the fractal dimension of a state in a general quantum system were introduced by one of the present authors (MO) in order to characterize chaotic properties of general states.In this paper, we show that -entropy of a state includes Kolmogorov's -entropy, and that the fractal dimension of a state describes fractal structure of Gaussian measures.     

Slicing, Chopping, and Path Conditions with Barriers

One of the critiques on program slicing is that slices presented to the user are hard to understand. This is mainly related to the problem that slicing dumps the results onto the user without any explanation. This work will present an approach that can be used to filter slices. This approach basically introduces barriers which are not allowed to be passed during slice computation. An earlier filtering approach is chopping which is also extended to obey such a barrier. The barrier variants of slicing and chopping provide filtering possibilities for smaller slices and better comprehensibility. The concept of barriers is then applied to path conditions, which provide necessary conditions under which an influence between the source and target criterion exists. Barriers make those conditions more precise.     

Proving total correctness of nondeterministic programs in infinitary logic

Summary It is shown how the weakest precondition approach to proving total correctness of nondeterministic programs can be formalized in infinitary logic. The weakest precondition technique is extended to hierarchically structured programs by adding a new primitive statement for operational abstraction, the nondeterministic assignment statement, to the guarded commands of Dijkstra. The infinitary logic L ₁ is shown to be strong enough to express the weakest preconditions for Dijkstra's guarded commands, but too weak for the extended guarded commands. Two possible solutions are considered: going to the essentially stronger infinitary logic L ₁₁ and restricting the power of the nondeterministic assignment statement in a way which allows the weakest preconditions to be expressed in L ₁.