Logic Programming L13.3 13.3 Asynchronous Connectives A logial constant or connective is asynchronous if its right rule can always be applied eagerly without loosing completeness. For example, A & B is asynchronous, because the rule ∆ ` A true ∆ ` B true ∆ ` A&B true &R can always be used for a conjunctive goal A&B, rather than first applying a left rule to an assumption ∆ or the using a clause...

Structural induction schemes have been used for mechanically proving properties of self-recursive concepts in previous research. However, based on those schemeq, it becomes very difficult to automatically generate the right induction hypotheses whenever the conjectures are involved with mutually recursive concepts. This paper will show that the difficulties come mainly from the weak induction s...

The "chain-store paradox" of Reinhard Sehen is one of a number of scenarios involving the finite repetition of a certain kind of sub-game about which a paradoxical conclusion can be derived. In each of these cases, a backward-induction argument is used to prove that it is futile to try to establish a reputation for cooperative or punitive behavior through appropriate action in the early stages ...

The induction-guided falsification searches a bounded reachable state space of a transition system for a counterexample that the system satisfies an invariant property. If no counterexamples are found, it tries to verify that the system satisfies the property by mathematical induction on the structure of the reachable state space of the system, from which some other invariant properties may be ...

Recall that some of the substitution rules mentioned the function FV : {λ-terms} → Var: FV(x) = {x} FV(e1 e2) = FV(e1) ∪ FV(e2) FV(λx. e) = FV(e)− {x}. Why does this definition uniquely determine the function FV? There are two issues here: • Existence: whether FV is defined on all λ-terms; • Uniqueness: whether the definition is unique. Of relevance here is the fact that there are three clauses...

We extend the work presented in [7, 8] to a regions-based, twodimensional, Euclidean theory. The goal is to recover the classical continuum on a point-free basis. We first derive the Archimedean property for a class of readily postulated orientations of certain special regions, “generalized quadrilaterals” (intended as parallelograms), by which we cover the entire space. Then we generalize this...

This paper deals with the control of the induction phase of anesthesia. The objective during this first phase is to bring the patient from its awake state to a final state corresponding to some given depth of anesthesia, measured by the BIS (Bispectral index), within a minimum time. This optimal time control strategy is addressed by means of the maximum principle of Pontryagin. Furthermore, sin...

Traditional induction variables (IV) analyses focus on computing the closed form expressions of variables. This paper presents a new IV analysis based on an IV property called distance interval . This property captures the value changes of a variable along a given controlflow path of a program. Based on distance intervals, an efficient algorithm detects dependences for array accesses that invol...

Recall that some of the substitution rules mentioned the function FV : {λ-terms} → Var: FV(x) = {x} FV(e1 e2) = FV(e1) ∪ FV(e2) FV(λx. e) = FV(e)− {x}. Why does this definition uniquely determine the function FV? There are two issues here: • Existence: whether FV is defined on all λ-terms; • Uniqueness: whether the definition is unique. Of relevance here is the fact that there are three clauses...