Canonical proof nets for classical logic

Proof nets provide abstract counterparts to sequent proofs modulo rule permutations; the idea being that if two proofs have the same underlying proof-net, they are in essence the same proof. Providing a convincing proof-net counterpart to proofs in the classical sequent calculus is thus an important step in understanding classical sequent calculus proofs. By convincing, we mean that (a) there should be a canonical function from sequent proofs to proof nets, (b) it should be possible to check the correctness of a net in polynomial time, (c) every correct net should be obtainable from a sequent calculus proof, and (d) there should be a cut-elimination procedure which preserves correctness. Previous attempts to give proof-net-like objects for propositional classical logic have failed at least one of the above conditions. In Richard McKinley (2010) [22], the author presented a calculus of proof nets (expansion nets) satisfying (a) and (b); the paper defined a sequent calculus corresponding to expansion nets but gave no explicit demonstration of (c). That sequent calculus, called LK∗ in this paper, is a novel one-sided sequent calculus with both additively and multiplicatively formulated disjunction rules. In this paper (a self-contained extended version of Richard McKinley (2010) [22]), we give a full proof of (c) for expansion nets with respect to LK∗, and in addition give a cut-elimination procedure internal to expansion nets – this makes expansion nets the first notion of proof-net for classical logic satisfying all four criteria.

Logic gates using high Rydberg states

Connected logic gates can be operated on the levels of one molecule by making use of the special properties of high Rydberg states. Explicit experimental results for the NO molecule are provided as an example. A number of other options, including that of several gates concatenated so as to operate as a full adder, are discussed. Specific properties of high Rydberg states that are used are: their autoionization is delayed so that they can be distinguished from direct multiphoton ionization, during their long life such states also can decay by energy transfer to the molecular core in a way that can be controlled by the judicious application of very weak external electrical fields, and the Rydberg states can be detected by the application of an ionizing electrical field. The combination of two (or three) color photons with and without external weak fields allows the construction of quite elaborate logic circuit diagrams and shows that taking advantage of the different intramolecular dynamics of levels that differ by their excitation enables the compounding of logic operations on one molecular frame.

Structure-activity relationships derived by machine learning: the use of atoms and their bond connectivities to predict mutagenicity by inductive logic programming.

We present a general approach to forming structure-activity relationships (SARs). This approach is based on representing chemical structure by atoms and their bond connectivities in combination with the inductive logic programming (ILP) algorithm PROGOL. Existing SAR methods describe chemical structure by using attributes which are general properties of an object. It is not possible to map chemical structure directly to attribute-based descriptions, as such descriptions have no internal organization. A more natural and general way to describe chemical structure is to use a relational description, where the internal construction of the description maps that of the object described. Our atom and bond connectivities representation is a relational description. ILP algorithms can form SARs with relational descriptions. We have tested the relational approach by investigating the SARs of 230 aromatic and heteroaromatic nitro compounds. These compounds had been split previously into two subsets, 188 compounds that were amenable to regression and 42 that were not. For the 188 compounds, a SAR was found that was as accurate as the best statistical or neural network-generated SARs. The PROGOL SAR has the advantages that it did not need the use of any indicator variables handcrafted by an expert, and the generated rules were easily comprehensible. For the 42 compounds, PROGOL formed a SAR that was significantly (P < 0.025) more accurate than linear regression, quadratic regression, and back-propagation. This SAR is based on an automatically generated structural alert for mutagenicity.

Bulūgh al-arab bi-taḥrīr al-nisab / li-Mawlānā al-Imām al-ʻAllāmah al-Humām Sībawayh zamānih wa-Farīd ʻaṣrih wa-awānih al-Shaykh Shihāb al-Dīn Aḥmad al-Ghunaymī al-Anṣārī : manuscript, [1622]

According to a muqābalah note on f. 11r, copy is collated with the author's copy in the presence of the author. The author signed the copy in his handwriting in the last days of Shaʻbān 1031 AH [June 1622 AD].

Lógica de D. Andres Piquer ...

Mode of access: Internet.

Logica de D. Andres Piquer ...

Mode of access: Internet.

A primer of logic,

Mode of access: Internet.

Elements of logic, together with an introductory view of philosophy in general, and a preliminary view of the reason. By Henry P. Tappan.

Mode of access: Internet.

A compendium of logic.

"Errata": p. [1] at end.

D. Francisci Toleti, Societatis Iesu, Commentaria vna cum quaestionibus in vniversam Aristotelis logicam : ornatius quàm ante hac, ac plus quàm mille in locis emendatiùs excusa, varijsqúe annotationibus, ad rem planè necessarijs insigniter illustrata /

Includes indexes.

Elements of logic; together with an introductory view of philosophy in general, and a preliminary view of the reason.

Mode of access: Internet.

Essai de logique judiciaire. : Ouvrage qui doit servir d'appréciation, et sur quelques points, d'antirrhatique [!] de la Logique judiciaire publiée à Paris, en 1841, par m. Hortensius de St.-Albin ... /

Mode of access: Internet.

Practical logic, or, The Art of thinking : a text-book for schools and colleges /

Mode of access: Internet.

An elementary treatise on logic ; including pt. I. Analysis of formulae. pt. II. Method. With an appendix of examples for analysis and criticism. And a copious index of terms and subjects. Designed for use in schools and colleges as well as for private study and use /

Mode of access: Internet.