We explore the formal foundations of recent studies comparing aural pattern recognition capabilities of populations of human and non-human animals. To date, these experiments have focused on the boundary between the Regular and Context-Free stringsets. We argue that experiments directed at distinguishing capabilities with respect to the Subregular Hierarchy, which subdivides the class of Regular stringsets, are likely to provide better evidence about the distinctions between the cognitive mechanisms of humans and those of other species. Moreover, the classes of the (...) Subregular Hierarchy have the advantage of fully abstract descriptive (model-theoretic) characterizations in addition to characterizations in more familiar grammar- and automata-theoretic terms. Because the descriptive characterizations make no assumptions about implementation, they provide a sound basis for drawing conclusions about potential cognitive mechanisms from the experimental results. We review the Subregular Hierarchy and provide a concrete set of principles for the design and interpretation of these experiments. (shrink)

Like modal logic, temporal logic, and description logic, separation logic has become a popular class of logical formalisms in computer science, conceived as assertion languages for Hoare-style proof systems with the goal to perform automatic program analysis. In a broad sense, separation logic is often understood as a programming language, an assertion language and a family of rules involving Hoare triples. In this survey, we present similarities between separation logic as an assertion language and modal and temporal logics. Moreover, we (...) propose a selection of landmark results about decidability, complexity and expressive power. (shrink)

We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. The translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. It is practically relevant because it makes it possible to use a decision procedure for the guarded fragment in order to decide regular grammar logics with (...) converse. The class of regular grammar logics includes numerous logics from various application domains. A consequence of the translation is that the general satisfiability problem for every regular grammar logics with converse is in EXPTIME. This extends a previous result of the first author for grammar logics without converse. Other logics that can be translated into GF2 include nominal tense logics and intuitionistic logic. In our view, the results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed-point operators. (shrink)