We propose a novel logic, Frame Logic (FL), that extends first-order logic and recursive definitions with construct Sp (·) captures the implicit supports of formulas—the precise subset universe upon which their meaning depends. Using such supports, we formulate proof rules facilitate frame reasoning elegantly when underlying model undergoes change. show is expressive by capturing several data-s...

We introduce PHFL, a probabilistic extension of higher-order fixpoint logic, which can also be regarded as temporal logics such PCTL and the $\mu^p$-calculus. show that PHFL is strictly more expressive than $\mu^p$-calculus, model-checking problem for finite Markov chains undecidable even $\mu$-only, order-1 fragment PHFL. Furthermore full far expressive: we give translation from Lubarsky's $\m...

logical form or covert syntax is a syntactic level introduced in recent generative approaches. using the ideas of first-order predicate logic, it interprets the strings whose elements cannot move in s–structure, because an element moves if it does not acquire its necessary scope. but unlike the predicate logic, logical form is based on syntactic principles and rules. therefore, logical form is ...