We prove that the observational equivalence of third-order finitary Idealized Algol is decidable using Game Semantics. By modelling the state explicitly in our games, we show that the denotation of a term M of this fragment of IA is a compactly innocent strategy-with-state, i.e. the strategy is generated by a finite view function fM. Given any such fM, we construct a real-time deterministic pushdown automaton that recognizes the complete plays of the knowing-strategy denotation of M. Since such plays characterize observational (...) equivalence, and there is an algorithm for deciding whether any two DPDAs recognize the same language, we obtain a procedure for deciding the observational equivalence of third-order finitary IA. Restricted to second-order terms, the DPDA representation cuts down to a deterministic finite automaton; thus our approach gives a new proof of Ghica and McCusker’s regular-expression characterization for this fragment. Our algorithmic representation of program meanings, which is compositional, provides a foundation for model-checking a wide range of behavioural properties of IA and other cognate programming languages. Another result concerns second-order IA with full recursion: we show that observational equivalence for this fragment is undecidable. (shrink)

Recent scholarship, focusing on the rapid decline of microscopy after the late 1680's, has shown that the limitations of microscopy and the ambivalent meaning of its findings led to a wide-spread sense of frustration with the new instrument. The present article tries to connect this fall from favor with the microscope's equally surprising but hitherto little noticed late rise to prominence. The crucial point is that when the microscope, more than a decade after the telescope, finally managed to arouse the (...) interest of natural philosophers, it did so as a corpuscularian tool, and as such it came to share the difficult fate of seventeenth-century corpuscularianism. The essay ends with the claim that the fall of microscopy was not only due to the failure of microscopy to corroborate corpuscularianism, but also to the changing definition of natural philosophy in the late seventeenth and early eighteenth centuries and to the separation of the domains of living matter from a physica whose recent mathematical framework excluded the organic world. (shrink)

Both Carnap and Quine made significant contributions to the philosophy of mathematics despite their diversedviews. Carnap endorsed the dichotomy between analytic and synthetic knowledge and classified certainmathematical questions as internal questions appealing to logic and convention. On the contrary, Quine wasopposed to the analytic-synthetic distinction and promoted a holistic view of scientific inquiry. The purpose of thispaper is to argue that in light of the recent advancement of experimental mathematics such as Monte Carlosimulations, limiting mathematical inquiry to the domain of (...) logic is unjustified. Robustness studies implemented inMonte Carlo Studies demonstrate that mathematics is on par with other experimental-based sciences. (shrink)

_ Source: _Volume 53, Issue 2-4, pp 294 - 321 Manuscript London, British Library, Burney 330 contains an anonymous collection of grammatical sophisms, dating in all probability from early 13th-century France or England, and all based on problematic biblical, liturgical or religious propositions. After a presentation of the manuscript and collection, this article examines two analysis tools that are applied in the majority of the sophisms, viz. a distinction between three layers of grammatico-semantic perfection or completeness, and the grammatical and (...) semantic supposition doctrines. It appears that these sophisms pay prominent attention to improper or figurative supposition, but are not intended for highly advanced readers. These preliminary results suggest that the Burney Sophismata Collection constituted an exercise tool to support textbook-based instruction in theological grammar, which was developed by such masters as Peter the Chanter and William de Montibus in the late 12th and early 13th centuries. (shrink)