Interpreting Strands in Linear Logic y

Interpreting Strands in Linear Logi

Linear Temporal Logic and Linear Dynamic Logic on Finite Traces

In this paper we look into the assumption of interpreting LTL over finite traces. In particular we show that LTLf , i.e., LTL under this assumption, is less expressive than what might appear at first sight, and that at essentially no computational cost one can make a significant increase in expressiveness while maintaining the same intuitiveness of LTLf interpreted over finite traces. Indeed, w...

Counting modulo Quantiiers on Nite Structures

We give a combinatorial method for proving elementary equivalence in rst-order logic FO with counting modulo n quantiiers D n. Inexpressibility results for FO(D n) with built-in linear order are also considered. For instance, the class of linear orders of length divisible by n + 1 cannot be expressed in FO(D n). Using this result we prove that comparing cardinalities or connectivity of ordered ...

Linear Formulas in Continuous Logic

We prove that continuous sentences preserved by the ultramean construction (a generalization of the ultraproduct construction) are exactly those sentences which are approximated by linear sentences. Continuous sentences preserved by linear elementary equivalence are exactly those sentences which are approximated in the Riesz space generated by linear sentences. Also, characterizations for linea...

Chu spaces as a semantic bridge between linear logic and mathematics

The motivating role of linear logic is as a “logic behind logic.” We propose a sibling role for it as a logic of transformational mathematics via the self-dual category of Chu spaces, a generalization of topological spaces. These create a bridge between linear logic and mathematics by soundly and fully completely interpreting linear logic while fully and concretely embedding a comprehensive ran...