We propose to augment intuitionistic linear with two new connectives to incorporate constraints drawn from a possibly continuous domain into linear logic expressions. The resulting formal language is called Constrained Intuitionistic Linear Logic (CIL L). Our ultimate goal is to capture physical properties of dynamically dexterous robotic systems within such a constraint domain while reasoning with changing state information through the representational strength of linear logic.
The resulting integration of linear, discrete reasoning with an encapsulation of dynamic properties of a system will be used to achieve behavioural planning of a fast, autonomous legged robot in complex outdoor environments. To this end, we will first formulate physically relevant semantics for CILL and prove the completeness and soundness of an associated proof theory. We will then adapt a number of existing solvers for real number and set constraints to adequately capture expressions that may arise from behavioural sequencing for dynamical systems. Finally, we will use the resulting language to encode behavioural sequencing problems for a legged robot and experimentally verify their relevance and correctness.
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