Why nonmonotonic logic?

The motivation for nonmonotonic logic is to produce a machine representation for default reasoning, broadly construed. In this paper we argue that all nonmonotonic logics have (by definition) inference rules that fail to preserve truth, and this fact leads to several undesirable features. In response to these problems, but recognizing the importance of the original motivation for nonmonotonic logic, we propose an alternative to nonmonotonic logic, which achieves nonmonotonicity of reasoning without abandoning in any way truth preserving inferences. This approach is based on a possible worlds framework, which we illustrate with a small Prolog program. Motivating this approach is an important distinction, which we believe the advocates of nonmonotonic logic to be ignoring: that between inferencing and making decisions, or equivalently that between inferencing and theory construction.     

FC-normal and extended stratified logic program

This paper investigates the consistency property of FC-normal logic program and presents an equivalent deciding condition whether a logic program P is an FC-normal program. The deciding condition describes the characterizations of FC-normal program. By the Petri-net presentation of a logic program, the characterizations of stratification of FC-normal program are investigated. The stratification of FC-normal program motivates us to introduce a new kind of stratification, extended stratification, over logic program. It is shown that an extended (locally) stratified logic program is an FC-normal program. Thus, an extended (locally) stratified logic program has at least one stable model. Finally, we have presented algorithms about computation of consistency property and a few equivalent deciding methods of the finite FC-normal program.     

Łukasiewicz logic and Riesz spaces

We initiate a deep study of Riesz MV-algebras which are MV-algebras endowed with a scalar multiplication with scalars from \([0,1]\) . Extending Mundici’s equivalence between MV-algebras and \(\ell \) -groups, we prove that Riesz MV-algebras are categorically equivalent to unit intervals in Riesz spaces with strong unit. Moreover, the subclass of norm-complete Riesz MV-algebras is equivalent to the class of commutative unital C \(^*\) -algebras. The propositional calculus \({\mathbb R}{\mathcal L}\) that has Riesz MV-algebras as models is a conservative extension of ?ukasiewicz \(\infty \) -valued propositional calculus and is complete with respect to evaluations in the standard model \([0,1]\) . We prove a normal form theorem for this logic, extending McNaughton theorem for ? ukasiewicz logic. We define the notions of quasi-linear combination and quasi-linear span for formulas in \({\mathbb R}{\mathcal L},\) and relate them with the analogue of de Finetti’s coherence criterion for \({\mathbb R}{\mathcal L}\) .     

Is the success of fuzzy logic really paradoxical?: Toward the actual logic behind expert systems

The formal concept of logical equivalence in fuzzy logic, while theoretically sound, seems impractical. The misinterpretation of this concept has led to some pessimistic conclusions. Motivated by practical interpretation of truth values for fuzzy propositions, we take the class (lattice) of all subintervals of the unit interval [0, 1] as the truth value space for fuzzy logic, subsuming the traditional class of numerical truth values from [0, 1]. The associated concept of logical equivalence is stronger than the traditional one. Technically, we are dealing with much smaller set of pairs of equivalent formulas, so that we are able to check equivalence algorithmically. The checking is done by showing that our strong equivalence notion coincides with the equivalence in logic programming. © 1996 John Wiley & Sons, Inc.     

A predicate spatial logic for mobile processes

A modal logic for describing temporal as well as spatial properties of mobileprocesses, expressed in the asynchronous π-calculus, is presented. The logic has recur-sive constructs built upon predicate-variables. The semantics of the logic is establishedand shown to be monotonic, thus guarantees the existence of fixpoints. An algorithm isdeveloped to automatically check if a mobile process has properties described as formulasin the logic. The correctness of the algorithm is proved.     

A spatial logic for concurrency—II

We present a modal logic for describing the spatial organization and the behavior of distributed systems. In addition to standard logical and temporal operators, our logic includes spatial operations corresponding to process composition and name hiding, and a fresh name quantifier. In Part I of this work we study the fundamental semantic properties of our logic; the focus of the present Part II is on proof theory. The main contributions are a sequent-based proof system for our logic, and a proof of cut-elimination for its first-order fragment.     

Is there a need for fuzzy logic?

“Is there a need for fuzzy logic?” is an issue which is associated with a long history of spirited discussions and debate. There are many misconceptions about fuzzy logic. Fuzzy logic is not fuzzy. Basically, fuzzy logic is a precise logic of imprecision and approximate reasoning. More specifically, fuzzy logic may be viewed as an attempt at formalization/mechanization of two remarkable human capabilities. First, the capability to converse, reason and make rational decisions in an environment of imprecision, uncertainty, incompleteness of information, conflicting information, partiality of truth and partiality of possibility - in short, in an environment of imperfect information. And second, the capability to perform a wide variety of physical and mental tasks without any measurements and any computations [L.A. Zadeh, From computing with numbers to computing with words - from manipulation of measurements to manipulation of perceptions, IEEE Transactions on Circuits and Systems 45 (1999) 105-119; L.A. Zadeh, A new direction in AI - toward a computational theory of perceptions, AI Magazine 22 (1) (2001) 73-84]. In fact, one of the principal contributions of fuzzy logic - a contribution which is widely unrecognized - is its high power of precisiation.Fuzzy logic is much more than a logical system. It has many facets. The principal facets are: logical, fuzzy-set-theoretic, epistemic and relational. Most of the practical applications of fuzzy logic are associated with its relational facet.In this paper, fuzzy logic is viewed in a nonstandard perspective. In this perspective, the cornerstones of fuzzy logic - and its principal distinguishing features - are: graduation, granulation, precisiation and the concept of a generalized constraint.A concept which has a position of centrality in the nontraditional view of fuzzy logic is that of precisiation. Informally, precisiation is an operation which transforms an object, p, into an object, p^∗, which in some specified sense is defined more precisely than p. The object of precisiation and the result of precisiation are referred to as precisiend and precisiand, respectively. In fuzzy logic, a differentiation is made between two meanings of precision - precision of value, v-precision, and precision of meaning, m-precision. Furthermore, in the case of m-precisiation a differentiation is made between mh-precisiation, which is human-oriented (nonmathematical), and mm-precisiation, which is machine-oriented (mathematical). A dictionary definition is a form of mh-precisiation, with the definiens and definiendum playing the roles of precisiend and precisiand, respectively. Cointension is a qualitative measure of the proximity of meanings of the precisiend and precisiand. A precisiand is cointensive if its meaning is close to the meaning of the precisiend.A concept which plays a key role in the nontraditional view of fuzzy logic is that of a generalized constraint. If X is a variable then a generalized constraint on X, GC(X), is expressed as X isr R, where R is the constraining relation and r is an indexical variable which defines the modality of the constraint, that is, its semantics. The primary constraints are: possibilistic, (r = blank), probabilistic (r = p) and veristic (r = v). The standard constraints are: bivalent possibilistic, probabilistic and bivalent veristic. In large measure, science is based on standard constraints.Generalized constraints may be combined, qualified, projected, propagated and counterpropagated. The set of all generalized constraints, together with the rules which govern generation of generalized constraints, is referred to as the generalized constraint language, GCL. The standard constraint language, SCL, is a subset of GCL.In fuzzy logic, propositions, predicates and other semantic entities are precisiated through translation into GCL. Equivalently, a semantic entity, p, may be precisiated by representing its meaning as a generalized constraint.By construction, fuzzy logic has a much higher level of generality than bivalent logic. It is the generality of fuzzy logic that underlies much of what fuzzy logic has to offer. Among the important contributions of fuzzy logic are the following:

1.

FL-generalization. Any bivalent-logic-based theory, T, may be FL-generalized, and hence upgraded, through addition to T of concepts and techniques drawn from fuzzy logic. Examples: fuzzy control, fuzzy linear programming, fuzzy probability theory and fuzzy topology.

2.

Linguistic variables and fuzzy if-then rules. The formalism of linguistic variables and fuzzy if-then rules is, in effect, a powerful modeling language which is widely used in applications of fuzzy logic. Basically, the formalism serves as a means of summarization and information compression through the use of granulation.

3.

Cointensive precisiation. Fuzzy logic has a high power of cointensive precisiation. This power is needed for a formulation of cointensive definitions of scientific concepts and cointensive formalization of human-centric fields such as economics, linguistics, law, conflict resolution, psychology and medicine.

4.

NL-Computation (computing with words). Fuzzy logic serves as a basis for NL-Computation, that is, computation with information described in natural language. NL-Computation is of direct relevance to mechanization of natural language understanding and computation with imprecise probabilities. More generally, NL-Computation is needed for dealing with second-order uncertainty, that is, uncertainty about uncertainty, or uncertainty² for short.

In summary, progression from bivalent logic to fuzzy logic is a significant positive step in the evolution of science. In large measure, the real-world is a fuzzy world. To deal with fuzzy reality what is needed is fuzzy logic. In coming years, fuzzy logic is likely to grow in visibility, importance and acceptance.     

基于Zelio logic的双电源加母联方案设计

双电源切换经常应用于一些重要场合,如电信移动基站、工厂、发电机组等。在此,基于施耐德Zelio logic逻辑控制器设计了详细的双电源加母联应用方案,希望能给用户提供借鉴。     

Notes on automata theory based on quantum logic

The main results are as follows: (1) it deals with a number of basic operations (concatenation, Kleene closure, homomorphism, complement); (2) due to a condition imposed on the implication operator for discussing some basic issues in orthomodular lattice-valued automata, this condition is investigated in detail, and it is discovered that all the relatively reasonable five implication operators in quantum logic do not satisfy this condition, and that one of the five implications satisfies such a condition iff the truth-value lattice is indeed a Boolean algebra; (3) it deals further with orthomodular lattice-valued successor and source operators; (4) an example is provided, implying that some negative results obtained in the literature may still hold in some typical orthomodular lattice-valued automata.     

A fuzzy logic system based on Schweizer-Sklar t-norm

In recent years, the basic research of fuzzy logic and fuzzy reasoning is growing ac- tively day by day, such as the basic logic system BL proposed by Hajek[1]; fuzzy logic system MTL proposed by Esteva and Godo[2]; fuzzy reasoning, implication operators …     

From logic programming towards multi‐agent systems

In this paper we present an extension of logic programming (LP) that is suitable not only for the “rational” component of a single agent but also for the “reactive” component and that can encompass multi‐agent systems. We modify an earlier abductive proof procedure and embed it within an agent cycle. The proof procedure incorporates abduction, definitions and integrity constraints within a dynamic environment, where changes can be observed as inputs. The definitions allow rational planning behaviour and the integrity constraints allow reactive, condition‐action type behaviour. The agent cycle provides a resource‐bounded mechanism that allows the agent’s thinking to be interrupted for the agent to record and assimilate observations as input and execute actions as output, before resuming further thinking. We argue that these extensions of LP, accommodating multi‐theories embedded in a shared environment, provide the necessary multi‐agent functionality. We argue also that our work extends Shoham’s Agent0 and the BDI architecture. This revised version was published online in June 2006 with corrections to the Cover Date.     

A characterization of answer sets for logic programs

Checking if a program has an answer set, and if so, compute its answer sets are just some of the important problems in answer set logic programming. Solving these problems using Gelfond and Lifschitz's original definition of answer sets is not an easy task. Alternative characterizations of answer sets for nested logic pro- grams by Erdem and Lifschitz, Lee and Lifschitz, and You et al. are based on the completion semantics and various notions of tightness. However, the notion of tightness is a local notion in the sense that for different answer sets there are, in general, different level mappings capturing their tightness. This makes it hard to be used in the design of algorithms for computing answer sets. This paper proposes a characterization of answer sets based on sets of generating rules. From this char- acterization new algorithms are derived for computing answer sets and for per- forming some other reasoning tasks. As an application of the characterization a sufficient and necessary condition for the equivalence between answer set seman- tics and completion semantics has been proven, and a basic theorem is shown on computing answer sets for nested logic programs based on an extended notion of loop formulas. These results on tightness and loop formulas are more general than that in You and Lin's work.     

基于F—logic的概念语义网

该文用Ｆ－ｌｏｇｉｃ程序写出了一个概念语义网Ｆ－Ｎｅｔ，从而指出了实现语义网的一种可能的新方法，用Ｆ－ｌｏｇｉｃ来实现语义网的优点是；可以利用Ｆ－ｌｏｇｉｃ程序对该语义网的语义网的语义模型进行了研究。而这一点现有的其它语义网实现方法都无法做到。     

On synthesis of 3 × 3 reversible logic functions

Reversible logic plays an important role in quantum computing. This article presents some novel results on synthesis of 3?×?3 reversible Boolean gates. We derive the relationship between reversible 3?×?3 gates and corresponding symmetric groups. By introducing a set of universal libraries, we show how to use group theory to synthesize any 3?×?3 reversible gate.     

Totally correct logic program transformations via well-founded annotations

We address the problem of proving the total correctness of transformations of definite logic programs. We consider a general transformation rule, called clause replacement, which consists in transforming a program P into a new program Q by replacing a set Γ ₁ of clauses occurring in P by a new set Γ ₂ of clauses, provided that Γ ₁ and Γ ₂ are equivalent in the least Herbrand model M(P) of the program P. We propose a general method for proving that transformations based on clause replacement are totally correct, that is, M(P)=M(Q). Our method consists in showing that the transformation of P into Q can be performed by: (i) adding extra arguments to predicates, thereby deriving from the given program P an annotated program $\overline{P}$ , (ii) applying a variant of the clause replacement rule and transforming the annotated program $\overline{P}$ into a terminating annotated program $\overline{Q}$ , and (iii) erasing the annotations from $\overline{Q}$ , thereby getting Q. Our method does not require that either P or Q are terminating and it is parametric with respect to the annotations. By providing different annotations we can easily prove the total correctness of program transformations based on various versions of the popular unfolding, folding, and goal replacement rules, which can all be viewed as particular cases of our clause replacement rule.     

Comments on “general failure of logic programs”

The paper [1] purports to present a classification of the general failure sets of logic programs and a simple proof of the theorem on the soundness and completeness of the negation-as-failure rule. In this note we clarify some conflicting terminology between [1] and the papers [2, 3] to which it predominantly refers. Our main purpose, however, is to point out major errors, in particular, one in the proof of the above mentioned theorem.     

BRAVE—a parallel logic language for artificial intelligence

This paper presents the first results for the implementation of the logic language BRAVE on a parallel architecture. We explain the operational semantics of BRAVE with common programming examples and show how both and and or parallelism can be exploited and controlled using BRAVE syntax. The design of an abstract machine for the parallel execution of BRAVE is given along with the principles of compilation and example codings. Results are presented from running example programs on a three-processor prototype, using an interpreter for BRAVE written in C.     

Revising Z: Part I – logic and semantics

This is the first of two related papers. We introduce a simple specification logic Z _C comprising a logic and a semantics (in ZF set theory) within which the logic is sound. We then provide an interpretation for (a rational reconstruction of) the specification language Z within Z _C . As a result we obtain a sound logic for Z, including a basic schema calculus. Received March 1998 / Accepted in revised form April 1999