Programming in temporal-nonmonotonic reasoning

Nonmonotonic reasoning has been proposed as an extension to classical first-order logic. Now people are interested in temporal reasoning with nonmonotonic logic [6]. We combine the monotonic logic [7] with a temporal logic to get a more general reasoning language. We discuss a monotonic logic TML which has predicate formulas, temporal formulas and a special modal formula, and give a completeness theorem of it. We use TH() to designate the set of theorems of a temporal-nonmonotonic theory which has the same language with TML. The completeness theorem of the temporal-nonmonotonic logic naturally arises. Like the relationship between predicate logic with a practical logic programming language PROLOG, we propose a useful temporal-nonmonotonic reasoning language TN for the temporal-nonmonotonic logic. As an appendix we supply an algorithm for the programming language TN.     

Implementing the ‘Fool's model’ of combinatory logic

This paper studies Fool's models of combinatory logic, and relates them to Hindley's D-completeness problem. A fool's model is a family of sets of formulas, closed under condensed detachment. Alternatively, it is a model ofCL in naive set theory. We examine Resolution; and the P-W problem. A sequel shows T is D-complete; also, its extensions. We close with an implementation FMO of these ideas.     

Toward a formal study of jazz chord sequences generated by Steedman’s grammar

This paper shows how to generate jazz chord sequences incrementally using Steedmans grammar by taking advantage of some formal properties. We point out the specific role played by particular chord sequences called cadential sequences. By precompiling them, one could improve the implementation of Steedmans grammar in a real-time improvisation system, and make it more reactive to the inputs of the user.I thank Mark Steedman for his comments on this text.     

A predicate transformer for the progress property ‘to-always’

The temporal property to-always has been proposed for specifying progress properties of concurrent programs. Although the to-always properties are a subset of the leads-to properties for a given program, to-always has more convenient proof rules and in some cases more accurately describes the desired system behavior. In this paper, we give a predicate transformerwta, derive some of its properties, and use it to define to-always. Proof rules for to-always are derived from the properties ofwta. We conclude by briefly describing two application areas, nondeterministic data flow networks and self-stabilizing systems where to-always properties are useful.     

Obvious inferences

The notion of obvious inference in predicate logic is discussed from the viewpoint of proof-checker applications in logic and mathematics education. A class of inferences in predicate logic is defined and it is proposed to identify it with the class of obvious logical inferences. The definition is compared with other approaches. The algorithm for implementing the obviousness decision procedure follows directly from the definition.     

Condensed detachment is complete for relevance logic: A computer-aided proof

The condensed detachment ruleD is a combination of modus ponens with a minimal amount of substitution. EarlierD has been shown to be complete for intuitionistic and classical implicational logic but incomplete forBCK andBCI logic. We show thatD is complete for the relevance logic. One of the main steps is the proof of the formula ((a a) a) a found in interaction with our resolution theorem prover. Various strategies of generating consequences of the axioms and choosing best ones for the next iteration were tried until the proof was found.     

Information Gaps as Communication Needs: A New Semantic Foundation for Some Non-Classical Logics

Semantics connected to some information based metaphor are well-known in logic literature: a paradigmatic example is Kripke semantic for Intuitionistic Logic. In this paper we start from the concrete problem of providing suitable logic-algebraic models for the calculus of attribute dependencies in Formal Contexts with information gaps and we obtain an intuitive model based on the notion of passage of information showing that Kleene algebras, semi-simple Nelson algebras, three-valued ukasiewicz algebras and Post algebras of order three are, in a sense, naturally and directly connected to partially defined information systems. In this way wecan provide for these logic-algebraic structures a raison dêetre different from the original motivations concerning, for instance, computability theory.     

Finiteness in Infinite-Valued Łukasiewicz Logic

In this paper we deepen Mundici's analysis on reducibility of the decision problem from infinite-valued ukasiewicz logic to a suitable m-valued ukasiewicz logic _m , where m only depends on the length of the formulas to be proved. Using geometrical arguments we find a better upper bound for the least integer m such that a formula is valid in if and only if it is also valid in _m. We also reduce the notion of logical consequence in to the same notion in a suitable finite set of finite-valued ukasiewicz logics. Finally, we define an analytic and internal sequent calculus for infinite-valued ukasiewicz logic.     

Logic programming and Σ-programming

We consider the main similarities and dissimilarities between logic programming and -programming. Particular emphasis is placed on efficient implementation of -programs. Algorithms that translate logic programs into -programs and back are given.Translated from Kibernetika, No. 1, pp. 67–72, January–February, 1989.     

Physically touching and tasting virtual objects enhances the realism of virtual experiences

Experiment 1 explored the impact of physically touching a virtual object on how realistic the virtual environment (VE) seemed to the user. Subjects in a no touch group picked up a 3D virtual image of a kitchen plate in a VE, using a traditional 3D wand. See and touch subjects physically picked up a virtual plate possessing solidity and weight, using a technique called tactile augmentation. Afterwards, subjects made predictions about the properties of other virtual objects they saw but did not interact with in the VE. See and touch subjects predicted these objects would be more solid, heavier, and more likely to obey gravity than the no touch group. In Experiment 2 (a pilot study), subjects physically bit a chocolate bar in one condition, and imagined biting a chocolate bar in another condition. Subjects rated the event more fun and realistic when allowed to physically bite the chocolate bar. Results of the two experiments converge with a growing literature showing the value of adding physical qualities to virtual objects. This study is the first to empirically demonstrate the effectiveness of tactile augmentation as a simple, safe, inexpensive technique with large freedom of motion for adding physical texture, force feedback cues, smell and taste to virtual objects. Examples of practical applications are discussed.Based in part on Physically touching virtual objects using tactile augmentation enhances the realism of virtual environments' by Hunter Hoffman which appeared in the Proceedings of the IEEE Virtual Reality Annual International Symposium '98, Atlanta GA, pp 59–63. ¢ 1998 IEEE.     

On generators and generative capacity of EOL forms

Summary In this paper we study the generative capacity of EOL forms from two different points of view. On the one hand, we consider the generative capacity of special EOL forms which one could call linear like and context free like, establishing the existence of a rich variety of non-regular sub-EOL language families. On the other hand, we propose the notion of a generator L of a language family We mean by this that any synchronized EOL system generating L generates — if understood as an EOL form — all languages of . We characterize the generators of the family of regular languages, and prove that other well known language families do not have generators.Partially supported under NSE Research Council of Canada, grant No. A-7700     

Explanation-based interpretation of open-textured concepts in logical models of legislation

In this paper we discuss a view of the Machine Learning technique called Explanation-Based Learning (EBL) or Explanation-Based Generalization (EBG) as a process for the interpretation of vague concepts in logic-based models of law.The open-textured nature of legal terms is a well-known open problem in the building of knowledge-based legal systems. EBG is a technique which creates generalizations of given examples on the basis of background domain knowledge. We relate these two topics by considering EBG's domain knowledge as corresponding to statute law rules, and EBG's training example as corresponding to a precedent case.By making the interpretation of vague predicates as guided by precedent cases, we use EBG as an effective process capable of creating a link between predicates appearing as open-textured concepts in law rules, and predicates appearing as ordinary language wording for stating the facts of a case.Standard EBG algorithms do not change the deductive closure of the domain theory. In the legal context, this is only adequate when concepts vaguely defined in some law rules can be reformulated in terms of other concepts more precisely defined in other rules. We call theory reformulation the process adopted in this situation of complete knowledge.In many cases, however, statutory law leaves some concepts completely undefined. We then propose extensions to the EBG standard that deal with this situation of incomplete knowledge, and call theory revision the extended process. In order to fill in knowledge gaps we consider precedent cases supplemented by additional heuristic information. The extensions proposed treat heuristics represented by abstraction hierarchies with constraints and exceptions.In the paper we also precisely characterize the distinction between theory reformulation and theory revision by stating formal definitions and results, in the context of the Logic Programming theory.We offer this proposal as a possible contribution to cross fertilization between machine learning and legal reasoning methods.     

A Hyperbase for Binary Lattice Hyperidentities

We define an identity to be hypersatisfied by a variety V if, whenever the operation symbols of V, are replaced by arbitrary terms (of appropriate arity) in the operations of V, the resulting identity is satisfied by V in the usual sense. Whenever the identity is hypersatisfied by a variety V, we shall say that is a V hyperidentity. For example, the identity x + x y = x (x + y) is hypersatisfied by the variety L of all lattices. A proof of this consists of a case-by-case examination of { + , } {x, y, x y, x y}, the set of all binary lattice terms. In an earlier work, we exhibited a hyperbase ^L for the set of all binary lattice (or, equivalently, quasilattice) hyperidentities of type 2, 2. In this paper we provide a greatly refined hyperbase _L . The proof that _L is a hyperbase was obtained by using the automated reasoning program Otter 3.0.4.     

Minimization of norms and logarithmic norms by diagonal similarities

It is a commonly occurring problem to find good norms · or logarithmic norms (·) for a given matrix in the sense that they should be close to respectively the spectral radius (A) and the spectral abscissa (A). Examples may be the certification thatA is convergent, i.e. (A)A<1 or stable, i.e. (A)(A)<0. Often the ordinary norms do not suffice and one would like to try simple modifications of them such as using an ordinary norm for a diagonally transformed matrix. This paper treats this problem for some of the ordinary norms.

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Minimisierung von Normen und Logarithmischen Normen durch Diagonale Transformationen

Zusammenfassung Ein oft vorkommendes praktisches Problem ist die Konstruktion von guten Normen · und logarithmischen Normen (·) für eine gegebene MatrixA. Mit gut wird dann verstanden, daß A den Spektralradius (A)=max |₁| und (A) die Spektralabszisse (A)=max Re _i gut approximieren. Beispiele findet man für konvergente Matrizen wo (A)A<1 gewünscht ist, und für stabile Matrizen wo (A)(A)<0 zu zeigen ist. Wir untersuchen hier, wie weit man mit Diagonaltransformationen und dengewöhnlichsten Normen kommen kann.

     

One Connection between Standard Invariance Conditions on Modal Formulas and Generalized Quantifiers

The language of standard propositional modal logic has one operator ( or ), that can be thought of as being determined by the quantifiers or , respectively: for example, a formula of the form is true at a point s just in case all the immediate successors of s verify .This paper uses a propositional modal language with one operator determined by a generalized quantifier to discuss a simple connection between standard invariance conditions on modal formulas and generalized quantifiers: the combined generalized quantifier conditions of conservativity and extension correspond to the modal condition of invariance under generated submodels, and the modal condition of invariance under bisimulations corresponds to the generalized quantifier being a Boolean combination of and .     

A set-theoretic translation method for polymodal logics

The paper presents aset-theoretic translation method for polymodal logics that reduces derivability in a large class of propositional polymodal logics to derivability in a very weak first-order set theory . Unlike most existing translation methods, the one we propose applies to any normal complete finitely axiomatizable polymodal logic, regardless of whether it is first-order complete or an explicit semantics is available. The finite axiomatizability of allows one to implement mechanical proof-search procedures via the deduction theorem. Alternatively, more specialized and efficient techniques can be employed. In the last part of the paper, we briefly discuss the application ofset T-resolution to support automated derivability in (a suitable extension of) .This work has been supported by funds MURST 40 and 60%. The second author was supported by a grant from the Italian Consiglio Nazionale delle Ricerche (CNR). A previous version of this paper has appeared as a research report in the ILLC-series, ML-94-09, University of Amsterdam. A short version is to be presented at STACS '95 in Munich.On leave at ILLC, Universiteit van Amsterdam, Plantage Muidergracht, 24, 1018 TV Amsterdam, The Netherlands.     

On Some Alleged Misconceptions about Fuzzy Logic

Entemann (2002) defends fuzzy logic by pointing to what he calls misconceptions concerning fuzzy logic. However, some of these ;misconceptions are in fact truths, and it is Entemann who has the misconceptions. The present article points to mistakes made by Entemann in three different areas. It closes with a discussion of what sort of general considerations it would take to motivate fuzzy logic.     

Relevant logic programming

In this paper we present a fragment of (positive) relevant logic which can be computed by a straightforward extension to SLD resolution while allowing full nesting of implications. These two requirements lead quite naturally to a fragment in which the major feature is an ambiguous user-level conjunction which is interpreted intensionally in query positions and extensionally in assertion positions. These restrictions allow a simple and efficient extension to SLD resolution (and more particularly, the PROLOG evaluation scheme) with quite minor loss in expressive power.     

Dynamic interpretation and hoare deduction

In this paper we present a dynamic assignment language which extends the dynamic predicate logic of Groenendijk and Stokhof [1991: 39–100] with assignment and with generalized quantifiers. The use of this dynamic assignment language for natural language analysis, along the lines of o.c. and [Barwise, 1987: 1–29], is demonstrated by examples. We show that our representation language permits us to treat a wide variety of donkey sentences: conditionals with a donkey pronoun in their consequent and quantified sentences with donkey pronouns anywhere in the scope of the quantifier. It is also demonstrated that our account does not suffer from the so-called proportion problem.Discussions about the correctness or incorrectness of proposals for dynamic interpretation of language have been hampered in the past by the difficulty of seeing through the ramifications of the dynamic semantic clauses (phrased in terms of input-output behaviour) in non-trivial cases. To remedy this, we supplement the dynamic semantics of our representation language with an axiom system in the style of Hoare. While the representation languages of barwise and Groenendijk and Stokhof were not axiomatized, the rules we propose form a deduction system for the dynamic assignment language which is proved correct and complete with respect to the semantics.Finally, we define the static meaning of a program of the dynamic assignment language as the weakest condition such that terminates successfully on all states satisfying , and we show that our calculus gives a straightforward method for finding static meanings of the programs of the representation language.