A class of interval-based temporal languages for uniformly representing and reasoning about actions and plans is presented. Actions are represented by describing what is true while the action itself is occurring, and plans are constructed by temporally relating actions and world states. The temporal languages are members of the family of Description Logics, which are characterized by high expressivity combined with good computational properties. The subsumption problem for a class of temporal Description Logics is investigated and sound and complete decision procedures are given. The basic language TL-F is considered #rst: it is the composition of a temporal logic TL # able to express interval temporal networks # together with the non-temporal logic F # a Feature Description Logic. It is proven that subsumption in this language is an NP-complete problem. Then it is shown how to reason with the more expressive languages TLU-FU and TL-ALCF . The former adds disjunction both at...

Applications of fuzzy logic in heuristic control have been highly successful, but which aspects of fuzzy logic are essential to its practical usefulness? This paper shows that an apparently reasonable version of fuzzy logic collapses mathematically to two-valued logic. Moreover, there are few if any published reports of expert systems in real-world use that reason about uncertainty using fuzzy logic. It appears that the limitations of fuzzy logic have not been detrimental in control applications because current fuzzy controllers are far simpler than other knowledge-based systems. In the future, the technical limitations of fuzzy logic can be expected to become important in practice, and work on fuzzy controllers will also encounter several problems of scale already known for other knowledge-based systems. 1

Answers to two old questions are given in this paper. 1. Modal logic S4, which was informally specified by Gödel in 1933 as a logic for provability, meets its exact provability interpretation. 2. Brouwer-Heyting-Kolmogorov realizing operations (1931-32) for intuitionistic logic Int also get exact interpretation as corresponding propositional operations on proofs; both S4 and Int turn out to be complete with respect to this proof realization. These results are based on operational reading of S4, where a modality is split into three operations. The logic of proofs with these operations is shown to be arithmetically complete with respect to the intended provability semantics and sufficient to realize every operation on proofs admitting propositional specification in arithmetic.

At the Dutch station Hoorn{Kersenboogerd, computer equipment is used for the safe and in time movement of trains. The computer equipment can be divided in two layers. A top layer o ering an interface and means to help a human operator in scheduling train movement. And a bottom layer which checks whether commands issued by the top layer can safely be executed by the rail hardware and which acts appropriately on detection of a hazardous situation. The bottom layer is implemented with a programmable piece of equipment namely a Vital Processor Interlocking1 (VPI). This paper introduces the most important features of the VPI at Hoorn{Kersenboogerd. This particular VPI is modelled in CRL. Furthermore, the paper touches upon correctness criteria and tool support for VPIs, and suggests ways for veri cation of properties of VPIs. Experiments show that it is indeed possible to e ciently verify these correctness criteria. 1991 Mathematics subject classi cation: 68Q40, 68Q45.

We show how labelled deductive systems can be combined with a logical framework to provide a natural deduction implementation of a large and well-known class of propositional modal logics (including K, D, T , B, S4, S4:2, KD45, S5). Our approach is modular and based on a separation between a base logic and a labelling algebra, which interact through a fixed interface. While the base logic stays fixed, different modal logics are generated by plugging in appropriate algebras. This leads to a hierarchical structuring of modal logics with inheritance of theorems. Moreover, it allows modular correctness proofs, both with respect to soundness and completeness for semantics, and faithfulness and adequacy of the implementation. We also investigate the tradeoffs in possible labelled presentations: We show that a narrow interface between the base logic and the labelling algebra supports modularity and provides an attractive proof-theory (in comparision to, e.g., semantic embedding) but limits th...

We present a technique that transforms any binary programming problem with integral coefficients to a satisfiability problem of propositional logic in linear time. Preliminary computational experience using this transformation, shows that a pure logical solver can be a valuable tool for solving binary programming problems. In a number of cases it competes favourably with well known techniques from operations research, especially for hard unsatisfiable problems. CR Subject Classification (1991): F.4: Mathematical Logic and Formal Languages; G.2: Discrete Mathematics. AMS Subject Classification (1991): 03B05: Classical Propositional Logic; 90C10: Integer Programming. Keywords & Phrases: Linear inequalities, Conjunctive Normal Form, Horn cardinality clauses. 1 Introduction The satisfiability problem of propositional logic (SAT) is considered important in many disciplines, such as mathematical logic, electrical engineering, computer science and operations research. It is the original ...

Linear and other relevant logics have been studied widely in mathematical, philosophical and computational logic. We describe a logical framework, RLF, for defining natural deduction presentations of such logics. RLF consists in a language together, in a manner similar to that of Harper, Honsell and Plotkin's LF, with a representation mechanism: the language of RLF is the lL-calculus; the representation mechanism is judgements-as-types, developed for relevant logics. The lL-calculus type theory is a first-order dependent type theory with two kinds of dependent function spaces: a linear one and an intuitionistic one. We study a natural deduction presentation of the type theory and establish the required proof-theoretic meta-theory. The RLF framework is a conservative extension of LF. We show that RLF uniformly encodes (fragments of) intuitionistic linear logic, Curry's l I -calculus and ML with references. We describe the Curry-Howard-de Bruijn correspondence of the lL-calculus with a s...

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. We define a value-based modal -calculus, built from firstorder formulas, modalities, and fixed point operators parameterized by data variables, which allows to express temporal properties involving data. We interpret this logic over Crl terms defined by linear process equations. The satisfaction of a temporal formula by a Crl term is translated to the satisfaction of a first-order formula containing parameterized fixed point operators. We provide proof rules for these fixed point operators and show their applicability on various examples. 1 Introduction In recent years we have applied process algebra in numerous settings [4, 8, 12]. The first lesson we learned is that process algebra pur sang is not very handy, and we need an extension with data. This led to the language Crl (micro Common Representation Language) [13]. The next observation was that it is very convenient to eliminate the parallel operator from a process description and reduce it to a very restricted form, whi...

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