We illustrate TeQsim, a qualitative simulator for continuous dynamical systems that combines the expressive power of qualitative diierential equations with temporal logic to constrain and reene the resulting predicted behaviors. Temporal logic is used to specify constraints that restrict the simulation to a region of the state space and to specify trajectories for input variables. A proposition...

A supervisory hybrid system may be modeled from two levels: logic level (upper) and continuous level (lower). In this paper, adaptive fuzzy Petri nets and neural networks are combined together for supervisory hybrid system modeling. Adaptive Fuzzy Petri Net is adopted to model the supervisory logic parts, and dynamic neural networks are applied to continuous parts. Two hybrid system examples ar...

Our reasoning is clearly fuzzy, so why is crisp logic so often adequate? We explain this phenomenon by showing that in the presence of noise, an arbitrary continuous (e.g., fuzzy) system can be well described by its discrete analog. However, as the description gets more accurate, the continuous description becomes necessary. 1 Formulation of the Problem Fuzzy logic is needed. Our reasoning is c...

This chapter addresses the problem of controlling a dynamical process using a hybrid controller, i.e., a controller that combines continuous dynamics with discrete logic. Typically, the discrete logic is used to effectively switch between several continuous controls laws and is called a supervisor. We review several tools that can be found in the literature to design this type of hybrid control...

In this paper, an adaptive fuzzy tracking control approach is proposed for a class of single-inputsingle-output (SISO) nonlinear systems in which the unknown continuous functions may be nonlinearlyparameterized. During the controller design procedure, the fuzzy logic systems (FLS) in Mamdani type are applied to approximate the unknown continuous functions, and then, based on the minimal learnin...

Proposed in this paper is extended continuous logic (ECL), a generalization of continuous logic based on the introduction of variable degree of conjunction and disjunction in complex conjunctive and disjunctive statements. The properties of ECL, as an algebraic structure, are analysed and various ECL functions are defined and classified. The apparatus of sentential algebra in ECL is defined wit...

Recent development of mathematical fuzzy logic is brieey surveyed. The set of all formulas of predicate logic that are tautologies with respect to all continuous t-norms is shown to be heavily non-recursive ((2-hard).

Continuous Markovian Logic (CML) is a multimodal logic that expresses quantitative and qualitative properties of continuous-time labelled Markov processes with arbitrary (analytic) state-spaces, henceforth called continuous Markov processes (CMPs). The modalities of CML evaluate the rates of the exponentially distributed random variables that characterize the duration of the labeled transitions...

Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of mathematical objects that can be described in classical first-order logic. The present paper shows that probabilistic computation (sometimes called randomize...