Conjointement, nous présentons trois-quatre artistes associés quant à leurs exigences et leur extrême volonté de continuer, et comme valeur architecturale (Barto & Barto), et comme valeur affranchie (Xatrec), et comme valeur contemporaine (Mathieu Mercier).

Rossii︠a︡. Folʹklor v trudakh Rozanova, Florenskogo, Trubet︠s︡kogo -- Ėmigrat︠s︡ii︠a︡. V rassei︠a︡nii sushchie ot Berlina do Tokio -- Russkai︠a︡ ėmigrat︠s︡ii︠a︡ i i︠a︡ponskiĭ folʹklor.

This paper presents an extended version of the Quantified Argument Calculus (Quarc). Quarc is a logic comparable to the first-order predicate calculus. It employs several nonstandard syntactic and semantic devices, which bring it closer to natural language in several respects. Most notably, quantifiers in this logic are attached to one-place predicates; the resulting quantified constructions are then allowed to occupy the argument places of predicates. The version presented here is capable of straightforwardly translating natural-language sentences involving defining clauses. A three-valued, (...) model-theoretic semantics for Quarc is presented. Interpretations in this semantics are not equipped with domains of quantification: they are just interpretation functions. This reflects the analysis of natural-language quantification on which Quarc is based. A proof system is presented, and a completeness result is obtained. The logic presented here is capable of straightforward translation of the classical first-order predicate calculus, the translation preserving truth values as well as entailment. The first-order predicate calculus and its devices of quantification can be seen as resulting from Quarc on certain semantic and syntactic restrictions, akin to simplifying assumptions. An analogous, straightforward translation of Quarc into the first-order predicate calculus is impossible. (shrink)

We investigate the expressive power of second-order logic over finite structures, when two limitations are imposed. Let SAA ) be the set of second-order formulas such that the arity of the relation variables is bounded by k and the number of alternations of second-order quantification is bounded by n . We show that this imposes a proper hierarchy on second-order logic, i.e. for every k , n there are problems not definable in AA but definable in AA for some c (...) 1 , d 1 . The method to show this is to introduce the set AUTOSAT of formulas in F which satisfy themselves. We study the complexity of this set for various fragments of second-order loeic. For first-order logic FOL with unbounded alternation of quantifiers AUTOSAT is PSpace complete. For first-order logic FOL n with alternation of quantifiers bounded by n , AUTOSAT is definable in AA . AUTOSAT) is definable in AA for some c 1 , d 1. (shrink)

The original Specker–Blatter theorem (1983) was formulated for classes of structures $\mathcal {C}$ of one or several binary relations definable in Monadic Second Order Logic MSOL. It states that the number of such structures on the set $[n]$ is modularly C-finite (MC-finite). In previous work we extended this to structures definable in CMSOL, MSOL extended with modular counting quantifiers. The first author also showed that the Specker–Blatter theorem does not hold for one quaternary relation (2003).If the vocabulary allows a constant (...) symbol c, there are n possible interpretations on $[n]$ for c. We say that a constant c is hard-wired if c is always interpreted by the same element $j \in [n]$. In this paper we show: (i)The Specker–Blatter theorem also holds for CMSOL when hard-wired constants are allowed. The proof method of Specker and Blatter does not work in this case.(ii)The Specker–Blatter theorem does not hold already for $\mathcal {C}$ with one ternary relation definable in First Order Logic FOL. This was left open since 1983.Using hard-wired constants allows us to show MC-finiteness of counting functions of various restricted partition functions which were not known to be MC-finite till now. Among them we have the restricted Bell numbers $B_{r,A}$, restricted Stirling numbers of the second kind $S_{r,A}$ or restricted Lah-numbers $L_{r,A}$. Here r is a non-negative integer and A is an ultimately periodic set of non-negative integers. (shrink)

We present a simplification and a modification of a method introduced by Herzig to prove the decidability of Quine’s ordered fragment of first-order logic. The method consists in an interpretation of quantifiers as modal operators. We show that our modification yields the decidability of two new ordered fragments of first-order logic, called the grooved fragment and the loosely grooved fragment, whose expressive power lies between Quine’s ordered fragment and the fluted fragment.

This study concerns an inventory of books, dated 1428/29, inscribed in Sofia, Dujčev gr. 253 (olim Kosinitsa 265), fol. 290r. Although the text was obscurely published in 1886, the vicissitudes of this codex over the following century impeded further research and the inventory continues to be overlooked in studies of Byzantine libraries, books and reading. A new edition, furnishing corrections and filling lacunae, together with a first translation and palaeographical analysis, provide a foundation for introducing this rare document and re-evaluating (...) its context and significance. While the limited prior scholarship generally presumed compilation in a monastic library in 1428/29 and pursued inquiries based on that surmise, examination of Dujčev gr. 253 draws attention to annotations by a member of the Laskaris Leontares family, dated 1431-1437,which place the codex in private possession during this period. A survey of thirteen extant codices variously connected to this distinguished aristocratic dynasty, c.1400 - 1455, elucidates acquisition, ownership and use of books in this socio-cultural milieu, with particular reference to this family’s history and social networks. Comparative assessment of this sample of thirteen codices and the 21 items recorded in the book-list of 1428/29 affirms the view that it relates to a private rather than an institutional library and distinguishes its potential value for investigating aristocratic book culture in the late Byzantine era. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:[Quaestio prima: quomodo est anima omnia]“Anima quodammodo est omnia.”2Verbum Philosophi est et abbreviatum; non autem omnibus satis manifestum. Quid me, Vir Dei,3 iam sollicitas in isto? Scis enim quod imperitussum scientia, et iste sermo profunda forte indiget exquisitione. Quaeris ergo specificari tibi illud quod dico ‘quodammodo’; quomodo enim erit anima omnia? Istum modum velles tibi specificari: autin summa dictione una, aut secundum singula entia singulos modos explicare.Videtur ergo ipse (...) Philosophus declarare istam propositionem inductive sic:‘sensus est quodammodo sensibilia, intellectus est quodammodo intelligibilia’,4igitur etc.[Obiectiones]Hic statim duo obicis:Primum quod cum anima tres partes habeat – vegetativam, sensitivam,intellectivam – in hac ostensione Philosophi ipsum vegetativum nulli entium attribuitur per quodammodo essendi idem, ergo videtur quod non debeatdicere: anima simpliciter quodammodo est omnia, sed secundum aliquas parteseius solum.Item, videtur quod debeat dici quod solum intellectivum sit quodammmodo omnia; nam omnia omnino sunt intelligibilia: universalia, singularia. Omnes naturae vere et simpliciter intelligibiles sunt quantum in ipsis est, licet prima et remotissima principia a nobis non intelligantur. Defectus enim in nobis est sicut in oculis vespertilionis, quibus non videt solem.[2] Item, quomodo est sensus ipsa sensibilia et intellectus ipsa intelligibilia?Aeque enim ignotae sunt hae assumptiones sicut et conclusio. Nam sensitivum res vivens est et substantia; sensibilia, res non-viventes et accidentia, qualitates de tertia specie qualitatis.5 Quomodo ergo est haec illa? Iam enim patet quod non conveniunt nisi in esse et ente tantum; in nullo enim genereomnino. Igitur videtur quod nihil sit dictu ‘sensus est quodammodo sensibilia’.Nam multo magis proprie et vere dictum videretur si diceret quis ‘homoquodammodo est asinus’, nam haec conveniunt in genere et generibus.Similiter, quaeris ex parte intellectus et intelligibilium. Intelligibilia enimsunt et substantiae et accidentia, et res viventes et non-viventes; ipsum autem intellectivum, solum substantia et res vivens.[Prima responsio Philosophi ad obiectionem secundam: Sensus est in potentia tale quale sensibile in actu]6Vir Dei, dices mihi, colligendo ex ipso eodem auctore, et respondebis |A 281vb| mihi cum quaero: sensus quomodo est ipsum sensibile? Respondebis cum Philosopho, quia hoc modo, scilicet quod ‘sensus est in potentia tale quale est ipsum sensibile in actu’,7 et illud pertractabis ad singulos sensus et sensibilia. Sic visus est in potentia tale quale est ipsum visibile in actu, et ita de aliis.Sed ego contra: Vir Dei, si ‘sensus est in potentia tale etc.’, ergo aliquando erit in actu tale, etc.Ad idem: sentire quoddam pati est et quaedam alteratio. Est enim sensus de genere virtutum passivarum secundum eundem Philosophum.8 Agens autem et patiens in principio sunt dissimilia; in fine vero, cum passum est, sunt similia.Igitur sensitivum ex quo sentiendo quodammodo patitur et passivum est. Infine cum passum est, simile erit ipsi activo, scilicet sensibili. Tunc igitur erit‘sensus tale in actu quale est etiam ipsum sensibile in actu’.Sed nunc quaero quid hoc sit dictu, scilicet quod aliquando ipsum sensitivum in actu sit tale quale ipsum sensibile. Quid dicis ‘tale quale’? Numquid si actu video colorem, est virtus visiva oculi mei actu color? Aut non dicis talis estcolor? Quaero, si in qualitate assimilabitur illa virtus visiva actu colori, nihil videtur huiusmodi expositio. |E 107vb| Sicut enim superius dictum est, non videntur convenire nisi in solo ente et esse.9Confiteor, Vir Dei, quia haec ultimo obiecta tentativa sunt, sed necessaria tamen ad propositum si recte dissolvantur, per gratiam ergo Dei et per orationes tuas, Vir Dei, spero ad haec quandoque redire.[Secunda responsio Philosophi ad obiectionem secundam: homo ut mundus minor]Sed nec illud quod legimus videtur sufficere ad propositum problema, Vir Dei: ‘homo est quodammodo omnis creatura et mundus’, minor scilicet,10 et communicans cum omnibus creaturis, hoc modo: “esse cum lapidibus, vivere cum plantis, sentire cum brutis, intelligere cum angelis,” et tandem cum Deo.11Si secundum hunc modum velim praedictum sermonem exponere, non erit.. (shrink)

Dans les Communia salmantins -- la plus vaste compilation didactique latine médiévale connue à ce jour et que l'on peut nommer ainsi, d'après la localisation du manuscrit depuis le XVe siècle, même si ces Points communs tirent vraisemblablement leur origine de la Faculté des arts de l'Université de Paris --, ces sections sur les philosophies morale et naturelle sont encadrées par celles, en cours d'édition et de traduction, sur la logique (Nova Logica, Vetus Logica) et sur la grammaire (de Priscien, (...) Institutiones grammaticae, XVII-XVIII, I-XVI). Ce livre -- qui présente commodément les éditions et les traductions en colonnes parallèles, tout en étant complété par une liste des tableaux et illustrations de meme qu'un index des noms -- fait donc partie d'un ensemble dont la publication est destinée à enrichir significativement notre connaissance de l'exégèse des corpus aristotélicien, boécien et priscianien, ainsi que celle de l'enseignement dialectique, par questions et réponses, des disciplines philosophiques dans l'institution universitaire du siècle d'or de la scolastique, au meme titre que le célèbre Guide de l'étudiant (parisien) du manuscrit Ripoll 109 auquel il s'apparente."--Publisher's description. (shrink)

This paper describes a decision procedure for disjunctions of conjunctions of anti-prenex normal forms of pure first-order logic (FOLDNFs) that do not contain V within the scope of quantifiers. The disjuncts of these FOLDNFs are equivalent to prenex normal forms whose quantifier-free parts are conjunctions of atomic and negated atomic formulae (= Herbrand formulae). In contrast to the usual algorithms for Herbrand formulae, neither skolemization nor unification algorithms with function symbols are applied. Instead, a procedure is described that rests on (...) nothing but equivalence transformations within pure first-order logic (FOL). This procedure involves the application of a calculus for negative normal forms (the NNF-calculus) with A -||- A & A (= &I) as the sole rule that increases the complexity of given FOLDNFs. The described algorithm illustrates how, in the case of Herbrand formulae, decision problems can be solved through a systematic search for proofs that reduce the number of applications of the rule &I to a minimum in the NNF-calculus. In the case of Herbrand formulae, it is even possible to entirely abstain from applying &I. Finally, it is shown how the described procedure can be used within an optimized general search for proofs of contradiction and what kind of questions arise for a &I-minimal proof strategy in the case of a general search for proofs of contradiction. (shrink)

A process-oriented model of belief is presented which permits the representation of nested propositional attitudes within first-order logic. The model (NIM, for nested intensional model) is axiomatized, sense-based (via intensions), and sanctions inferences involving nested epistemic attitudes, with different agents and different times. Because NIM is grounded upon senses, it provides a framework in which agents may reason about the beliefs of another agent while remaining neutral with respect to the syntactic forms used to express the latter agent's beliefs. Moreover, (...) NIM provides agents with a conceptual map, interrelating the concepts of knowledge, belief, truth, and a number of cognate concepts, such as infers, retracts, and questions. The broad scope of NIM arises in part from the fact that its axioms are represented in a novel extension of first-order logic, -FOL (presented herein). -FOL simultaneously permits the representation of truth ascriptions, implicit self-reference, and arbitrarily embedded sentences within a first-order setting. Through the combined use of principles derived from Frege, Montague, and Kripke, together with context-sensitive semantic conventions, -FOL captures the logic of truth inferences, while avoiding the inconsistencies exhibited by Tarski. Applications of -FOL and NIM to interagent reasoning are described and the soundness and completeness of -FOL are established herein. (shrink)

This ar ti cle is di vided into three parts. In the first part Kant´s ar gu men ta tion fol low ing all the steps given in Fundamentación III is ex - plained. The com monly ac cepted in ter nal di vi - sion was fol lowed, and not the sets of para graphs in di cated by Mc Car thy. In the sec ond..

In November 2014 I had the pleasure of examining Bruxellensis 11377–80. This paper manuscript was owned by Pierre Pantin at his death in 1611; it occupies no. 30 in his catalogue, where the first text, on fols 1–4, was misidentified as ‘Hymni Homeri’. The next owner, André Schott, repeated the error; Omont uses a page-numeration that completely excludes the current fols 1–4.

After a brief sketch of the state of Buridan studies, this review article examines the recent study, by Benoît Patar, of a commentary on Aristotle’s Physics that is generally attributed to Albert of Saxony, but which Patar believes to have been authored by John Buridan (the text is preserved in the manuscript Bruges, Stadsbibliotheek 477, fols. 60va–163vb, and was edited by Patar himself in 1999). Patar is utterly convinced that the Bruges Quaestiones represent Buridan’s prima lectura, that is, his first (...) course of lectures on the Physics, which preceded the two other redactions that are traditionally attributed to him. However, there is no textual evidence in support of this assumption, but only speculative circumstantial evidence. The article therefore rejects Patar’s thesis as highly problematic. (shrink)

There exist valuable methods for theorem proving in non classical logics based on translation from these logics into first-order classical logic (abbreviated henceforth FOL). The key notion in these approaches istranslation from aSource Logic (henceforth abbreviated SL) to aTarget Logic (henceforth abbreviated TL). These methods are concerned with the problem offinding a proof in TL by translating a formula in SL, but they do not address the very important problem ofpresenting proofs in SL via a backward translation. We propose a (...) framework for presenting proofs in SL based on a partial backward translation of proofs obtained in a familiar TL: Order-Sorted Predicate Logic. The proposed backward translation transfers some formulasF TL belonging to the proof in TL into formulasF SL , such that the formulasF SL either (a) belong to a corresponding deduction in SL (in the best case) or, (b) are semantically related in some precise way, to formulas in the corresponding deduction in SL (in the worst case). The formulasF TL andF SL can obviously be considered aslemmas of their respective proofs. Therefore the transfer of lemmas of TL gives at least a skeleton of the corresponding proof in SL. Since the formulas of a proof keep trace of the strategy used to obtain the proof, clearly the framework can also help in solving another fundamental and difficult problem:the transfer of strategies from classical to non classical logics. We show how to apply the proposed framework, at least to S5, S4(p), K, T, K4. Two conjectures are stated and we propose sufficient (and in general satisfactory) conditions in order to obtain formulas in the proof in SL. Two particular cases of the conjectures are proved to be theorems. Three examples are treated in full detail. The main lines of future research are given. (shrink)

Kit Fine has argued that the Tarski Semantics for the language of first order logic is inadequate. A semantic theory for FOL is inadequate if there are formulae of FOL whose meanings or satisfaction conditions it cannot compositionally account for. It is argued here that Fine’s case against Tarski rests on a mistake.

Modern knowledge of the grammarian Consentius’ De barbarismis et metaplasmis, a work valuable for the study of the Latin language, dates back to a relatively recent past: it was only in 1817 that its editio princeps was published by Ph.C. Buttmann, just a few years after the legal scholar A.W. Cramer came across a mention of the then unknown treatise in a ninth-century MS in the Bayerische Staatsbibliothek of Munich, numbered Clm 14666. Based on this solitary manuscript, H. Keil published (...) the short treatise in the fifth volume of his Grammatici Latini. With no little enthusiasm did W.M. Lindsay announce his unearthing of what, in his own words, had ‘long been a “desideratum”, a second authority’ for this text, in the MS F 15 III d at the Universitätsbibliothek Basel; this was followed by E.O. Winstedt's complete collation and M. Niedermann's critical edition. After about a century now there comes to light a third authority, surprisingly enough in a codex which has enjoyed such fame in the past decades that one might wonder how Consentius could have gone unnoticed in it for so long: this is the eleventh-century MS of Venice, Biblioteca Nazionale Marciana Lat. Z. 497, in which the De barbarismis et metaplasmis is contained on fols. 84vb 39 - 90va 39; moreover, a so-far-unnoticed quotation from it, together with one from Consentius’ De nomine et uerbo, is found on fol. 41vb 16–21 of the same manuscript in a famous grammatical florilegium. The codex, written in Romanesque minuscule and probably originating in Rome, is regarded as a handbook of liberal arts designed by Lawrence Archbishop of Amalfi, formerly a monk at Montecassino, thereafter a teacher in Florence and Rome, where he died in about 1049. Based on palaeographical evidence, F.L. Newton rightfully assumed as an exemplar for this codex a MS in Beneventan script, as some features can be detected that betray the scribal imitation of that typical South Italian script, namely the use of the distinctive abbreviation for eius as ‘ei in ligature with stroke through the descender of the i’, the Beneventan ti ligature for the assibilated sound, and the 2-shaped Beneventan interrogation sign, to which I would add the typical abbreviation for in as a long i cut by a horizontal stroke and the confusion of a and t. Interestingly enough, none of these features is found on fols. 66–95, those containing the new Consentius: from a codicological point of view, this is an autonomous section, written by a different scribe from the rest of the MS and preserving some grammatical texts generally attributed to insular authors, such as Smaragdus’ Liber in partibus Donati and part of the compilation entitled Pauca de barbarismo, which precedes the De barbarismis et metaplasmis; not surprisingly, the new text of Consentius displays numerous features of the Insular script, such as the symbols for enim, autem, eius, est, nihil and et. On this basis it is most likely that this whole section was never included in the Beneventan exemplar, but was added at the time and place of copying of our MS in order to enrich the grammatical content. (shrink)

The interpretability of AI is just as important as its performance. In the LegalAI field, there have been efforts to enhance the interpretability of models, but a trade-off between interpretability and prediction accuracy remains inevitable. In this paper, we introduce a novel framework called LK-IB for compulsory measure prediction (CMP), one of the critical tasks in LegalAI. LK-IB leverages Legal Knowledge and combines an Interpretable model and a Black-box model to balance interpretability and prediction performance. Specifically, LK-IB involves three steps: (...) (1) inputting cases into the first module, where first-order logic (FOL) rules are used to make predictions and output them directly if possible; (2) sending cases to the second module if FOL rules are not applicable, where a case distributor categorizes them as either “simple” or “complex“; and (3) sending simple cases to an interpretable model with strong interpretability and complex cases to a black-box model with outstanding performance. Experimental results demonstrate that the LK-IB framework provides more interpretable and accurate predictions than other state-of-the-art models. Given that the majority of cases in LegalAI are simple, the idea of model combination has significant potential for practical applications. (shrink)

In this paper I try to answer four basic questions: (1) How the concept of God is to be represented? (2) Are there any logical principles governing it? (3) If so, what kind of logic lies behind them? (4) Can there be a logic of the concept of God? I address them by presenting a formal-logical account to the concept of God. I take it as a methodological desideratum that this should be done within the simplest existing logical formalism. I (...) start with first-order logic (FOL) with identity, and then show that its simplest modal extension (SQML, or the simplest quantified modal logic) is enough for us to formalize a minimally satisfactory theory of the concept of God. I focus exclusively on the monotheistic concept of God. (shrink)

In his catalogue of the manuscripts of Grosseteste's writings S.H. Thomson attributed to him a number of sermons each of which is free standing and none of which belongs to the sermon collection made after the bishop's death. One of these is found in the British Library MS Harley 979, where it occupies fols 37va-39rb. It is written in seven columns, in a hand of the second half of the thirteenth century. This sermon on the commandments is ascribed to Grosseteste (...) in the hand of the scribe, with the words: «Sermo magistri Roberti Lincolniensis Episcopi de decem preceptis decalogi». It has not hitherto been published. (shrink)

Este artículo se divide en tres partes. En la primera se procura situar la argumentación de Kant siguiendo todos los pasos dados en la Fundamentación III. Se optó por seguir la división interna comunmente aceptada, y no los conjuntos de parágrafos indicados por McCarthy. En la segunda, se desarrolla la crítica rea li za da por Allison. En la tercera, finalmente, se discuten, breve y sintéticamente, tres interrogantes: i) la relación entre la libertad transcendental y el imperativo categórico; ii) el (...) problema del círculo vicioso oculto y iii) las dos fallas de la deducción de la libertad en Fundamentación III, identificadas por Allison, comparando su argumentación con la de McCarthy.This article is divided into three parts. In the first part Kant´s argumentation following all the steps given in Fundamentación III is explained. The commonly accepted internal division was fol lowed, and not the sets of para graphs indicated by McCarthy. In the second part, the criticism developed by Allison is developed. In the third part, three questions are quickly and syntheti cally discussed; i) the relation be tween transcenden tal liberty and the categorical imperitive; ii) the problem of the hid denviscious circle, and iii) two errors in the deduction of liberty in Fundamentación III, identified by Allison, comparing his argumentation with that of McCarthy. (shrink)

Gaze following occurs automatically in social interactions, but the degree to which gaze is followed depends on whether an agent is perceived to have a mind, making its behavior socially more relevant for the interaction. Mind perception also modulates the attitudes we have towards others, and deter-mines the degree of empathy, prosociality and morality invested in social interactions. Seeing mind in others is not exclusive to human agents, but mind can also be ascribed to nonhuman agents like robots, as long (...) as their appearance and/or behavior allows them to be perceived as intentional beings. Previous studies have shown that human appearance and reliable behavior induce mind perception to robot agents, and positively affect attitudes and performance in human-robot interaction. What has not been investigated so far is whether different triggers of mind perception have an independent or interactive effect on attitudes and performance in human-robot interaction. We examine this question by manipulating agent appearance (human vs. robot) and behavior (reliable vs. random) within the same paradigm and examine how congruent (human/reliable vs. robot/random) versus incongruent (human/random vs. robot/reliable) combinations of these triggers affect performance (i.e., gaze fol-lowing) and attitudes (i.e., agent ratings) in human-robot interaction. The results show that both ap-pearance and behavior affect human-robot interaction but that the two triggers seem to operate in iso-lation, with appearance more strongly impacting attitudes, and behavior more strongly affecting per-formance. The implications of these findings for human-robot interaction are discussed. (shrink)

The essential structure of proofs is proposed as the basis for a measure of complexity of formulas in FOL. The motivating idea was the recognition that distinct theorems can have the same derivation modulo some non essential details. Hence the difficulty in proving them is identical and so their complexity should be the same. We propose a notion of complexity of formulas capturing this property. With this purpose, we introduce the notions of schema calculus, schema derivation and description complexity of (...) a schema formula. Based on these concepts we prove general robustness results that relate the complexity of introducing a logical constructor with the complexity of the component schema formulas as well as the complexity of a schema formula across different schema calculi. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:A New Fragment of Sophocles and its Schedographic ContextJohn J. KeaneyThe General ContextA popular medium of elementary Byzantine education in grammar and orthography was the genre known as.1 The genre is represented by a (larger or smaller) collection of (brief passages of prose [most frequently] or verse). The individual words of the text are accompanied by a fourfold analysis: (1) interlinear glosses;2 (2 and 3) grammatical and etymological/derivational analysis (...) of individual words; (4) a list of words beginning with the same two or three letters as the word analyzed-each word may or may not be glossed. While these lists quote some well-known texts, the grammatical analyses preserve only two quotations of classical authors; both, by some chance, are of Sophocles.3Our earliest, and necessarily very incomplete, knowledge of the genre comes in references and allusions thereto, like those of Anna Comnena (Alexiad 15.7) or Eustathius (e.g., Comm. in Hom. Il. 1.367.4; [End Page 173] 2.585.16 van der Valk). Between that period and the appearance of the first texts, there arose a traditional core of (hereafter skhedē).4 The earliest representatives of this core were written in the south of Italy at the end of the thirteenth century. These, with the folia containing our text, are B (Barberinianus Graecus 102:1290/1 [subscription]: fol. 60 v); P (Parisinus Graecus 25745: fol. 61 r) written by Nicolaus Hagiopetrite\s in Galatina; N (Par. Gr. 2572:1295/6 [subscription]: fol. 51 v) by one Georgius, son of the protopapas Leo, of Ardeo; and M (Monacensis Graecus 272: fol. 42 v). These represent one6 branch of the oldest class of manuscripts (class Ia). The four manuscripts are related, as shown by the fact that they preserve the same order of skhedē throughout. N and M are closely related for they add a final skhedos not found in B and P. A second branch (Ib) is represented by Pal (Palatinus Graecus 927: fol. 26 v), R (Reginenses, PP Pii II 15: fol. 206 v8), and C (Conventi Soppressi 29: fol. 40 v).The Specific ContextThe ninth of the traditional skhedē is[End Page 174]The word analyzed is. The text:A.A.B.C.D. om. PalRAlthough the text is badly transmitted,10 it is all but certain that it goes back, ultimately, to Herodian.11 The closest parallel passage12 is from the Peri dikhronōn (2.15.11-27 Lehrs):[End Page 175] (δ 511).A. B. (F36 Kassel-Austin).Some Sophoclean Usage(1) is found once (Ph. 945). (2) With compare Ai. 543: and Ant. 548: (3) For the polarity of "mind" and, see OT 524-24: F 929.1-2 Radt:. For as a feature of the Sophoclean hero, see Knox 1964, 21.John J. KeaneyPrinceton University e-mail: [email protected], J., and J. Irigoin, eds. 1977. La Paléographie grecque et byzantine. Paris: Centre Nationale de la Recherche Scientifique. Google ScholarCanart, P. 1977. "Un Style d'écriture livresque dans les manuscrits chypriotes du XIVe siècle: La Chypriote 'bouclée.'" In Bompaire and Irigoin, 303-21.Constantinides, C. N., and R. Browning. 1993. Dated Greek Manuscripts from Cyprus to the Year 1570. Nicosia: Cyprus Research Center. Google ScholarDyck, A. 1993. "Aelius Herodian: Recent Studies and Prospects for Future Research." ANRW 2.34.1:772-94. Berlin: de Gruyter. Google Scholar---, ed. 1995. Epimerismi Homerici. 2d part. Sammlung griechischer und lateinischer Grammatiker 5/2. Berlin: de Gruyter. Google ScholarGallavotti, C. 1983. "Nota sulla schedographia di Moscopulo e suoi precedenti fino a Teodoro Prodromo." BPEC, 3d ser., 4:1-35. Google ScholarGamillscheg, E. 1950. "Zur handschriften Überlieferung byzantinischen Schulbücher." JÖB 43:211-30. Google ScholarHunger, H. 1978. Die hochsprachliche Literatur der Byzantiner. Vol. 2. Munich: C. H. Beck. [End Page 176]Google ScholarKassel, R., and C. Austin. 1991. Poetae Comici Graeci. Vol. 2. Berlin: de Gruyter. Google ScholarKeaney, J. J. 1971. "Moschopulea." BZ 63:303-21. Google ScholarKnox, B. M. W. 1964. The Heroic Temper. Berkeley and Los Angeles: University of California Press. Google ScholarLehrs, K... (shrink)

Any language $$\mathcal {L}$$ L of classical logic, of first- or higher-order, is expanded with sentential quantifiers and operators. The resulting language $$\mathcal {L}^+\!$$ L +, capable of self-reference without arithmetic or syntax encoding, can serve as its own metalanguage. The syntax of $$\mathcal {L}^+$$ L + is represented by directed graphs, and its semantics, which coincides with the classical one on $$\mathcal {L}$$ L, uses the graph-theoretic concepts of kernels and semikernels. Kernels provide an explosive semantics, while semikernels generalize (...) this to situations where paradoxes do not lead to explosion, thus distinguishing them from contradictions. Paradoxes arise only at the metalevel due to specific interpretations of the operators, but they can be avoided: $$\mathcal {L}^+$$ L + can express paradoxes but remains free from them. For an expansion $$\mathcal {L}^+$$ L + of any FOL language $$\mathcal {L}$$ L, with the non-explosive semantics, a complete reasoning system is obtained by extending Gentzen’s classical sequent calculus with two rules for the sentential quantifiers. Adding (cut) yields a complete system for the explosive semantics. The novel semantics and self-referential capabilities seem promising for a further extension of classical logic towards one capable also of consistently expressing its own syntax and truth theory. (shrink)

ABSTRACT The question of whether Wittgenstein was a liberal philosopher has received less attention than the question of whether he was a conservative philosopher but, as Robert Greenleaf Brice has recently argued, there are hints of liberalism in some of his remarks, and some philosophers, like Richard Eldridge, have argued that a kind of liberalism follows from Wittgenstein’s later philosophy. Richard Rorty has also drawn liberal conclusions from a philosophical viewpoint which draws on Wittgenstein’s work and Alice Crary has suggested (...) that the lessons learned from her own interpretation of Wittgenstein are “reflected in forms of social life that embody the ideals of liberal democracy”. Here I will argue both that Wittgenstein was not a liberal and that his philosophy does not imply a liberal viewpoint. The authors discussed here do not demonstrate that any broad ideological conclusions fol-low from Wittgenstein’s philosophical remarks. -/- RESUMEN La pregunta si Wittgenstein fue un filósofo liberal ha recibido menos atención que la de si fue un filósofo conservador, pero, como Robert Greenleaf Brice ha defendido recientemente, hay muchos indicios de liberalismo en algunas de sus observaciones, y algunos filó-sofos, como Richard Eldridge, han sostenido que hay un cierto tipo de liberalismo que se sigue de la filosofía de su última etapa. Richard Rorty ha sacado también conclusiones libera-les a partir de la perspectiva filosófica que se basa en la obra de Wittgenstein y Alice Crary ha sugerido que las lecciones aprendidas de su propia interpretación de Wittgenstein se “reflejan en formas de vida social que incorporan los ideales de la democracia liberal”. En este artículo, voy a defender tanto que Wittgenstein no era un liberal como que su filosofía no implica una perspectiva liberal. Los autores de que se discuten aquí no prueban que de las observaciones filosóficas de Wittgenstein se desprendan amplias conclusiones ideológicas de ningún tipo. (shrink)

Synthetic biology (SynBio) covers two main areas: application engineering, exemplified by metabolic engi- neering, and the design of life from artificial building blocks. As the general public is often reluctant to embrace synthetic approaches, preferring nature to artifice, its immediate future will depend very much on the public’s reaction to the unmet needs created by the pervasive demands of sustainability. On the other hand, this reluctance should not have a negative impact on research that will now take into account the (...) existence of the multiple transitions that cells face over time. The ages of life—birth, development, maturation, senescence and death—reflect specific key transitions and have, until now, rarely been taken into account in SynBio designs. This results in a mismatch between novelty and the very long evolutionary time that led to the existing chassis [remember that this is the common term used to describe the cellular framework as seen by synthetic biologists (de Lorenzo & Danchin, 2008)]. It also implies that, in general, transitions between growth stages will be taken into account with the appro- priate embodiment of highly specific processes. This is particularly important when adapting new models to their host, whether natural or artificial. Adaptation fol- lows two stages, short-term accommodation of new entities and long-term assimilation into the cell as a whole. This requires discrimination between classes of entities. We suggest that proteins playing the essential role of Maxwell’ demons, here named Maxwell’s dis- criminators (MxDs) to refer to their original function, will permit the assimilation and accommodation of artificial constructs. As a consequence, we can foresee that class discrimination, beyond mere recognition, will be implemented in SynBio 2.0, leading to an authentic par- adigm shift (Kuhn, 1996), based on conceptions that embody information as a genuine currency of reality. (shrink)

In this paper we analyse the conditions for attributing to AI autonomous systems the ontological status of “artificial moral agents”, in the context of the “distributed responsibility” between humans and machines in Machine Ethics (ME). In order to address the fundamental issue in ME of the unavoidable “opacity” of their decisions with ethical/legal relevance, we start from the neuroethical evidence in cognitive science. In humans, the “transparency” and then the “ethical accountability” of their actions as responsible moral agents is not (...) in contradiction with the unavoidable “opacity” (unawareness) of the brain process by which they perform their moral judgements on the right action to execute. In fact, the moral accountability of our actions depends on what is immediately before and after our “moral judgements” on the right action to execute (formally, deontic first order logic (FOL) decisions). I.e., our moral accountability depends on the “ethical constraints” we imposed to our judgement before performing it in an opaque way. Anyway, our moral accountability depends overall on the “ethical assessment” or explicit “moral reasoning” after and over the moral judgement before executing our actions (deontic higher order logic (HOL) assessment). In this way, in the light of the AI “imitation game”, the consistent attribution of the status of ethically accountable artificial moral agents to autonomous AI systems depends on two similar conditions. Firstly, it depends on the presence of “ethical constraints” to be satisfied in their Machine Learning (ML) supervised optimization algorithm during its training phase, to give the system ethical skills (“competences”) in its decisions. Secondly – and definitely—, it depends on the presence in an AI autonomous system of a deontic HOL “ethical reasoner” to perform an automatic, and fully transparent assessment (metalogical deontic valuation) about the decisions taken by the ethically skilled ML algorithm about the right action to execute, before executing it. Finally, we show that the proper deontic FOL and HOL for this class of artificial moral agents is Kripke’s modal relational logic, in its algebraic topological formalization. This is naturally implemented in the dissipative QFT unsupervised deep learning of our brains, based on the “doubling of the degrees of freedom” (DDF), and then in the so-called “deep-belief” artificial neural networks for the statistical data pre-processing. This unsupervised learning procedure is also compliant with the usage of the “maximin fairness principle”, used as a balancing aggregation principle of the statistical variables in Sen’s formal theory of fairness. (shrink)

We aim to compile some means for a rational reconstruction of a named part of the start-over of Baruch (Benedictus) de Spinoza's metaphysics in 'de deo' (which is 'pars prima' of the 'ethica, ordine geometrico demonstrata' ) in terms of 1st order model theory. In so far, as our approach will be judged successful, it may, besides providing some help in understanding Spinoza, also contribute to the discussion of some or other philosophical evergreen, e.g. 'ontological commitment'. For this text we (...) assume the reader familiar with 'de deo' as well as with some basic concepts and results of 1st order model theory. Before we start reconstruction, we will first revisit shortly the concept of 'attributum' (definitio IV) in it's setting in 'de deo' , next scan for formalizable aspects of 'in suo genere finita' ('de deo', definitio II), subsequently list the model theoretic constructs we will make use of. Then we begin reconstruction by stating "coordinative definitions" for the notions of 'attribute (of a substance)', 'modus (as conceived via an attribute)' and 'substance (as conceived via an attribute)', reasoning shortly for each of them. The "coordinative definitions", we will arrive at, must not be understood as literal translations of Spinoza's concepts - of course, there can't be such a thing as a literal translation - they are meant as formal analoga of these concepts, mapping some logical structure. But even with this caveat they may seem strange to the reader at this stage of discussion. Additional justification for them then should be found in our endeavour, to map some argumentation of Spinoza's proofs of some of his propositions from this starting point. -/- [ Version 1 of this paper originated from 2020-03-14. This is version 2 from 2021-09-12 with some readability amendments. ]. (shrink)

The purpose of this paper is to communicate - as a proposal - a general method of assigning a 'truthmaker' to any 1st order sentence in each of its models. The respective construct is derived from the standard model theoretic (recursive) satisfaction definition for 1st order languages and is a conservative extension thereof. The heuristics of the proposal (which has been somewhat idiosyncratic from the current point of view) and some more technical detail of the construction may be found in (...) my article on part I of Spinoza's 'ethica, ordine geometrico demonstrata', which is the context within which I elaborated the assignment. But this context need not be repeated here, the presentation of the truthmaker assignment will be comprehensible to anybody with solid basic knowledge in 1st order model theory, anything used is standard and no advanced techniques are required. (shrink)

In a recent article1 mention was made of a MS. from which Goetz printed selections in Vol. V. of the . This MS. was not used by Goetz. On fol. 81 appears the following entry: ‘Moechus est adulter alterius t[h]orum furtim polluens; inde a m echo dicitur m[o]echanica ars, ingeniosa atque subtilissima et p ene quomodo facta uel administrata sit inuisibilis in tantum, ut etiam uisum conspicientium quodam modo furetur, dum non facile penetratur eius ingeniositas quali ingenio artis candelabrum illud (...) Theodosianum factum legitur.’. (shrink)

A history of logic -- Patterns of reasoning -- A language and its meaning -- A symbolic language -- 1850-1950 mathematical logic -- Modern symbolic logic -- Elements of set theory -- Sets, functions, relations -- Induction -- Turning machines -- Computability and decidability -- Propositional logic -- Syntax and proof systems -- Semantics of PL -- Soundness and completeness -- First order logic -- Syntax and proof systems of FOL -- Semantics of FOL -- More semantics -- Soundness and (...) completeness -- Why is first order logic "First Order"? (shrink)

This is a survey of work on set-theoretical invariance criteria for logicality. It begins with a review of the Tarski-Sher thesis in terms, first, of permutation invariance over a given domain and then of isomorphism invariance across domains, both characterized by McGee in terms of definability in the language L∞,∞. It continues with a review of critiques of the Tarski-Sher thesis, and a proposal in response to one of those critiques via homomorphism invariance. That has quite divergent characterization results depending (...) on its formulation, one in terms of FOL, the other by Bonnay in terms of L∞,∞, both without equality. From that we move on to a survey of Bonnay’s work on similarity relations between structures and his results that single out invariance with respect to potential isomorphism among all such. Turning to the critique that calls for sameness of meaning of a logical operation across domains, the paper continues with a result showing that the isomorphism invariant operations that are absolutely definable with respect to KPU−Inf are exactly those definable in full FOL; this makes use of an old theorem of Manders. The concluding section is devoted to a critical discussion of the arguments for set-theoretical criteria for logicality. (shrink)

This article studies a fragment on the conic sections that appear in the Codex Atlanticus, fols. 611rb/915ra. Arguments are put forward to assemble these two folios. Their comparison with the Latin texts available before 1500 shows that they derive from the De speculis comburentibus of Alhacen and the De speculis comburentibus of Regiomontanus, joined together in his autograph manuscript. Having identified the sources, and discussed their mathematics, the issue of their transmission is targeted. It is shown that these notes were (...) written by Paolo dal Pozzo Toscanelli, through whom they reached the notebooks of Leonardo da Vinci. (shrink)

forall x: Calgary is a full-featured textbook on formal logic. It covers key notions of logic such as consequence and validity of arguments, the syntax of truth-functional propositional logic TFL and truth-table semantics, the syntax of first-order (predicate) logic FOL with identity (first-order interpretations), symbolizing English in TFL and FOL, and Fitch-style natural deduction proof systems for both TFL and FOL. It also deals with some advanced topics such as modal logic, soundness, and functional completeness. Exercises with solutions are available. (...) It is provided in PDF (for screen reading, printing, and a special version for dyslexics), HTML, and in LaTeX source code. (shrink)

Recent years have seen the appearance of many English-language hand books of logic and numerous monographs on topical discoveries in the foundations of mathematics. These publications on the foundations of mathematics as a whole are rather difficult for the beginners or refer the reader to other handbooks and various piecemeal contribu tions and also sometimes to largely conceived "mathematical fol klore" of unpublished results. As distinct from these, the present book is as easy as possible systematic exposition of the now (...) classical results in the foundations of mathematics. Hence the book may be useful especially for those readers who want to have all the proofs carried out in full and all the concepts explained in detail. In this sense the book is self-contained. The reader's ability to guess is not assumed, and the author's ambition was to reduce the use of such words as evident and obvious in proofs to a minimum. This is why the book, it is believed, may be helpful in teaching or learning the foundation of mathematics in those situations in which the student cannot refer to a parallel lecture on the subject. This is also the reason that I do not insert in the book the last results and the most modem and fashionable approaches to the subject, which does not enrich the essential knowledge in founda tions but can discourage the beginner by their abstract form. A. G. (shrink)

Many efforts have been made in recent years to construct formal systems for mechanizing general mathematical reasoning. Most of these systems are based on logics which are stronger than first-order logic. However, there are good reasons to avoid using full second-order logic for this task. In this work we investigate a logic which is intermediate between FOL and SOL, and seems to be a particularly attractive alternative to both: ancestral logic. This is the logic which is obtained from FOL by (...) augmenting it with the transitive closure operator. While the study of this logic has so far been mostly model-theoretical, this work is devoted to its proof theory. Two natural Gentzen-style proof systems for ancestral logic are presented: one for the reflexive transitive closure, and one for the non-reflexive one. We show that these systems are sound for ancestral logic and provide evidence that they indeed encompass all forms of reasoning for this logic that are used in practice. The two systems are shown to be equivalent by providing translation algorithms between them. We end with an investigation of two main proof-theoretical properties: cut elimination and constructive consistency proof. (shrink)

Semantic networks were developed in cognitive science and artificial intelligence studies as graphical knowledge representation and inference tools emulating human thought processes. Formal analysis of the representation and inference capabilities of the networks modeled them as subsets of standard first-order logic (FOL), restricted in the operations allowed in order to ensure the tractability that seemed to characterize human reasoning capabilities. The graphical network representations were modeled as providing a visual language for the logic. Sub-sets of FOL targeted on knowledge representation (...) came to be called description logics, and research on these logics has focused on issues of tractability of subsets with differing representation capabilities, and on the implementation of practical inference systems achieving the best possible performance. Semantic network research has kept pace with these developments, providing visual languages for knowledge entry, editing, and presenting the results of inference, that translate unambiguously to the underlying description logics. This paper discusses the design issues for such semantic network formalisms, and illustrates them through detailed examples of significant generic knowledge structures analyzed in the literature, including determinables, contrast sets, genus/differentiae, taxonomies, faceted taxonomies, cluster concepts, family resemblances, graded concepts, frames, definitions, rules, rules with exceptions, essence and state assertions, opposites and contraries, relevance, and so on. Such examples provide important test material for any visual language formalism for logic. (shrink)

This paper introduces two languages and associated logics designed to afford perspicuous representations of a range of natural language arguments involving adverbs and the like: first-order logic with basic adverbs (FOL-BA) and first-order logic with scoped adverbs (FOL-SA). The guiding logical idea is that an adverb can come between a term and the rest of the statement it is a part of, resulting in a logically stronger statement. I explain various interesting challenges that arise in the attempt to implement the (...) guiding idea, and provide solutions for some but not all of them. I conclude by outlining some directions for further research. (shrink)

Schubert’s proposal ([Sch00]) that sentences not only describe but also characterize situations is worked out in the context of Linear Temporal Logic (LTL), a well-known propositional logic with linear future operators (e.g. [HR04]). The resulting formalism LTL∗∗ illustrates an approach that diverges from Schubert’s FOL∗∗ in technical details but shares many (if not all) its motivations.

forall x: Dortmund is an adaptation and German translation of forall x: Calgary. As such, it is a full-featured textbook on formal logic. It covers key notions of logic such as consequence and validity, the syntax of truth-functional (propositional) logic and truth-table semantics, the syntax of first-order (predicate) logic with identity and first-order interpretations, formalizing German in TFL and FOL, and Fitch-style natural deduction proof systems for both TFL and FOL. It also deals with some advanced topics such as the (...) syntax and (Kripke-)semantics of modal logic. The book is provided in PDF and in LaTeX source code. A booklet with solutions for the exercises in the book is available. (shrink)

The manuscript Venice, Biblioteca Nazionale Marciana, Class XI n. 12, Zanetti Latini 301 (= 1576), contains on fols. 1r–24v a seemingly unique copy of a series of fifteen logical questions, ten on obligationes and the remaining five on insolubilia.1 The series on obligationes is untitled and unattributed in the manuscript, but the questions on insolubilia begin (fol. 18r11) “Incipiunt quaestiones super insolubilibus,” and are attributed at the end to a certain John of Wesel (fol. 24v41): “Ergo expletae sunt quaestiones insolubilium (...) a Johanne de Vesalia Parixius2 disputatae. Deo gratias. Amen.”. (shrink)

It has been strongly disputed that Philoponus is the author of the commentary on the third book of De Anima printed in vol. xv of CAG under his name, and Stephanus of Alexandria has been taken to be its real author. The evidence for the authorship of Stephanus is as follows: Codex Parisinus gr. 1914, written in the twelfth century, has an adscript by a later hand saying βιβλ⋯ον τρ⋯τον ⋯π⋯ ϕωνης στεϕ⋯νου, and the same appears in the fifteenth-century Codex (...) Estensis iii F 8. In 543.9 there is a clause saying ὡς ⋯ν τῷ περ⋯ ⋯ρμηνε⋯ας ⋯μ⋯θομεν, which was taken by M. Hayduck to be direct reference to Stephanus' commentary on the De Interpretatione, edited also by Hayduck in vol. xiii/3 of CAG. The third book, says Hayduck, is short and jejune, in contrast to the verbosity of the preceding two books. The commentary on the third book of De Anima is divided into lectures, but the first two books are not. Some locutions are used constantly in the third book and in Stephanus' in De Interpretatione as well. In the Codex Vaticanus gr. 241 fol. 6 we are told that Stephanus also wrote a commentary on the De Anima. (shrink)