Adjuncts elimination in the static ambient logic

The Ambient Logic (AL) has been proposed for expressing spatial properties of processes of the Mobile Ambient calculus (MA). Restricting both the calculus and the logic to their static part yields static ambients (SA) and the static ambient logic (SAL), that form a model for queries about semistructured data. SAL also includes the non-standard fresh quantifier (I). This work adresses the questions of expressiveness and minimality of SAL from the point of view of adjuncts. We define the intensional fragment of the logic (SALint), the logic without adjuncts, and prove that it captures all the expressiveness of the logic. We moreover study the question of adjuncts elimination in SAL∀, where I quantifier is replaced by the classical ∀ quantifier. We conclude with a proof of the minimality of SALint.