Logic Meets Algebra: Compositional Timing Analysis for Synchronous Reactive Multithreading

Towards a Fuzzy Context Logic

“…The proof follows immediately by (2). In summary, we needed (35) for proving idempotency (48) and the neutral element (51).…”

“…A t-norm 0, 1 ½ 2 ! 0, 1 ½ is a commutative (1), associative (2), and monotone function (3), with a neutral element 1 (4).…”

“…For the generalized fuzzy logic semantics, the lattice meet-operation ⊓ will be shown to fulfill the properties of a t-norm, the join-operation ⊔ , those of the corresponding s-norm. Both are required to be commutative (1), associative (2), and support an identity element (4) and monotonicity (3) (for the full proofs see Section 4.4). We prove monotonicity for ⊓ (38) and ⊔ (39): The operation ) with the definition…”

“…The mereologically interested reader may notice that adding even the weakened variant of the weak supplementation principle is sufficient to collapse context logic term structures to a single level by (2). The reason for this is that the weak supplementation principle considerably strengthens the expressiveness of negation, which given the principle always ensures the existence of a fully negative individual.…”

“…Fuzzy logic has been employed successfully in intelligent systems, sensoractuator systems, expert systems, and machine learning techniques for more than 50 years [1]. Being a tool for inference at both the logical and the sensor-actuator systems level its use for reliable and explainable autonomous systems has become a focus of recent research [2][3][4][5]. One key building block for this has been a growing understanding of fuzzy logic semantics over the past 20 years [6] and the position this family of logics assumes within the field of logics in general.…”