2017/06/10 by Valentín, Oriol
#03 #FOS: Computer and information sciences #Logic in Computer Science (cs.LO)
paper · doi:10.48550/arxiv.1706.03244
The displacement calculus D is a conservative extension of the Lambek calculus L1 (with empty antecedents allowed in sequents). L1 can be said to be the logic of concatenation, while D can be said to be the logic of concatenation and intercalation. In many senses, it can be claimed that D mimics L1 in that the proof theory, generative capacity and complexity of the former calculus are natural extensions of the latter calculus. In this paper, we strengthen this claim. We present the appropriate classes of models for D and prove some completeness results; strikingly, we see that these results and proofs are natural extensions of the corresponding ones for L1.