This paper studies proof systems for the logics of super-strict implication ST2–ST5, which correspond to C.I. Lewis’ systems S2–S5 freed of paradoxes of strict implication. First, Hilbert-style axiomatic systems are introduced and shown to be sound and complete by simulating STn in Sn and backsimulating Sn in STn, respectively(for n=2,...,5). Next, G3-style labelled sequent calculi are investigated. It is shown that these calculi have the good structural properties that are distinctive of G3-style calculi, that they are sound and complete, and (...) it is shown that the proof search for G3. ST2 is terminating and therefore the logic is decidable. (shrink)

Decidability of monadic first-order classical logic was established by Löwenheim in 1915. The proof made use of a semantic argument, but a purely syntactic proof has never been provided. In the present paper we introduce a syntactic proof of decidability of monadic first-order logic in innex normal form which exploits G3-style sequent calculi. In particular, we introduce a cut- and contraction-free calculus having a (complexity optimal) terminating proof-search procedure. We also show that this logic can be faithfully embedded in the (...) modal logic T. (shrink)

This paper studies proof systems for the logics of super-strict implication \(\textsf{ST2}\) – \(\textsf{ST5}\), which correspond to C.I. Lewis’ systems \(\textsf{S2}\) – \(\textsf{S5}\) freed of paradoxes of strict implication. First, Hilbert-style axiomatic systems are introduced and shown to be sound and complete by simulating \(\textsf{STn}\) in \(\textsf{Sn}\) and backsimulating \(\textsf{Sn}\) in \(\textsf{STn}\), respectively (for \({\textsf{n}} =2, \ldots, 5\) ). Next, \(\textsf{G3}\) -style labelled sequent calculi are investigated. It is shown that these calculi have the good structural properties that are distinctive (...) of \(\textsf{G3}\) -style calculi, that they are sound and complete, and it is shown that the proof search for \(\mathsf {G3.ST2}\) is terminating and therefore the logic is decidable. (shrink)

G3-style sequent calculi for the logics in the cube of non-normal modal logics and for their deontic extensions are studied. For each calculus we prove that weakening and contraction are height-preserving admissible, and we give a syntactic proof of the admissibility of cut. This implies that the subformula property holds and that derivability can be decided by a terminating proof search whose complexity is in Pspace. These calculi are shown to be equivalent to the axiomatic ones and, therefore, they are (...) sound and complete with respect to neighbourhood semantics. Finally, a Maehara-style proof of Craig’s interpolation theorem for most of the logics considered is given. (shrink)

In previous work by Baaz and Iemhoff, a Gentzen calculus for intuitionistic logic with existence predicate is presented that satisfies partial cut elimination and Craig's interpolation property; it is also conjectured that interpolation fails for the implication-free fragment. In this paper an equivalent calculus is introduced that satisfies full cut elimination and allows a direct proof of interpolation via Maehara's lemma. In this way, it is possible to obtain much simpler interpolants and to better understand and overcome the failure of (...) interpolation for the implication-free fragment. (shrink)

The paper presents an epistemic logic with quantification over agents of knowledge and with a syntactical distinction between de re and de dicto occurrences of terms. Knowledge de dicto is characterized as ‘knowledge that’, and knowlegde de re as ‘knowledge of’. Transition semantics turns out to be an adequate tool to account for the distinctions introduced.

This paper introduces the logics of super-strict implications, where a super-strict implication is a strengthening of C.I. Lewis' strict implication that avoids not only the paradoxes of material implication but also those of strict implication. The semantics of super-strict implications is obtained by strengthening the (normal) relational semantics for strict implication. We consider all logics of super-strict implications that are based on relational frames for modal logics in the modal cube. it is shown that all logics of super-strict implications are (...) connexive logics in that they validate Aristotle's Theses and (weak) Boethius's Theses. A proof-theoretic characterisation of logics of super-strict implications is given by means of G3-style labelled calculi, and it is proved that the structural rules of inference are admissible in these calculi. It is also shown that validity in the S5-based logic of super-strict implications is equivalent to validity in G. Priest's negation-as-cancellation-based logic. Hence, we also give a cut-free calculus for Priest's logic. (shrink)

A constructivisation of the cut-elimination proof for sequent calculi for classical, intuitionistic and minimal infinitary logics with geometric rules—given in earlier work by the second author—is presented. This is achieved through a procedure where the non-constructive transfinite induction on the commutative sum of ordinals is replaced by two instances of Brouwer’s Bar Induction. The proof of admissibility of the structural rules is made ordinal-free by introducing a new well-founded relation based on a notion of embeddability of derivations. Additionally, conservativity for (...) classical over intuitionistic/minimal logic for the seven (finitary) Glivenko sequent classes is here shown to hold also for the corresponding infinitary classes. (shrink)

This paper provides a proof-theoretic study of quantified non-normal modal logics. It introduces labelled sequent calculi based on neighbourhood semantics for the first-order extension, with both varying and constant domains, of monotone NNML, and studies the role of the Barcan formulas in these calculi. It will be shown that the calculi introduced have good structural properties: invertibility of the rules, height-preserving admissibility of weakening and contraction and syntactic cut elimination. It will also be shown that each of the calculi introduced (...) is sound and complete with respect to the appropriate class of neighbourhood frames. In particular, the completeness proof constructs a formal derivation for derivable sequents and a countermodel for non-derivable ones, and gives a semantic proof of the admissibility of cut. (shrink)

Starting from a proof-theoretic perspective, where meaning is determined by the inference rules governing logical operators, in this paper we primarily aim at developing a proof-theoretic alternative to the model-theoretic meaning-invariant logical pluralism discussed in Beall and Restall. We will also outline how this framework can be easily extended to include a form of meaning-variant logical pluralism. In this respect, the framework developed in this paper—which we label two-level proof-theoretic pluralism—is much broader in scope than the one discussed in Beall (...) and Restall’s book. (shrink)

This paper deals with the question of the logicality of modal logics from a proof-theoretic perspective. It is argued that if Dos̆en’s analysis of logical constants as punctuation marks is embraced, it is possible to show that all the modalities in the cube of normal modal logics are indeed logical constants. It will be proved that the display calculus for each displayable modality admits a purely structural presentation based on double-line rules which, following Dos̆en’s analysis, allows us to claim that (...) the corresponding modal operators are logical constants. (shrink)

We prove a generalization of Maehara’s lemma to show that the extensions of classical and intuitionistic first-order logic with a special type of geometric axioms, called singular geometric axioms, have Craig’s interpolation property. As a corollary, we obtain a direct proof of interpolation for (classical and intuitionistic) first-order logic with identity, as well as interpolation for several mathematical theories, including the theory of equivalence relations, (strict) partial and linear orders, and various intuitionistic order theories such as apartness and positive partial (...) and linear orders. (shrink)

Hasta el final de su vida, y durante más de diez años, Publio Virgilio Marón (70-19 a.C.) estuvo dedicado a la composición de la Eneida, unánimemente reconocida como el más perfecto exponente del clasicismo romano. Virgilio pretendió con ella ofrecer al público romano la gran epopeya de sus orígenes, que sirviera al tiempo como justificación y exaltación del nuevo régimen impuesto por el emperador Augusto. El resultado sería esta magistral combinación entre el pasado legendario de Roma y su historia reciente. (...) Más allá de las evidentes funciones políticas y sus distintos niveles temáticos, la Eneida nos ofrece la gesta de un héroe exiliado de su patria. Tras la quema de Troya a manos de los griegos, Eneas parte hacia una tierra extraña, en la que había de encontrar su nuevo hogar. En su viaje por mar, el hijo de Venus arrostrará numerosas dificultades hasta llegar a su destino en la costa italiana, e incluso allí se verá obligado a entablar una guerra contra los pueblos itálicos, para conseguir al fin fundar una ciudad llamada a convertirse en cabeza del mundo. (shrink)

How has the concept of democracy been understood, manifested, reimagined and represented through the ages? In a work that spans 2,500 years these fundamental questions are addressed by 66 experts, each contributing their overview of a theme applied to a period in history. With the help of a broad range of case material they illustrate the physical, social and cultural contexts of democracy in Western culture from antiquity to the present. Individual volume editors ensure the cohesion of the whole, and (...) to make it as easy as possible to use, chapter themes are identical across each of the volumes. Superbly illustrated, the full six-volume set combines to present the most comprehensive and authoritative survey available on democracy throughout history. The six volumes cover: 1 - Antiquity (500 BCE-565 CE); 2 - Medieval Age (565-1450); 3 - Renaissance (1450-1650); 4 - Age of Enlightenment (1650-1800); 5 - Age of Empire (1800-1920); 6 Modern Age (1920-present) The ten themes are: Sovereignty; Liberty and the Rule of Law; The 'Common Good'; Economic and Social Democracy; Religion and the Principles of Political Obligation; Citizenship and Gender; Ethnicity, Race and Nationalism; Democratic Crises, Revolutions and Civil Resistance; International Relations; Beyond the Polis. The page extent for the pack is approximately 2016pp. Each volume opens with Notes on Contributors and an Introduction and concludes with Notes, Bibliography, and an Index. The Cultural Histories Series A Cultural History of Democracy is part of The Cultural Histories Series. Titles are available both as printed hardcover sets for libraries needing just one subject or preferring a one-off purchase and tangible reference for their shelves, or as part of a fully-searchable digital library available to institutions by annual subscription or on perpetual access (see www.bloomsburyculturalhistory.com). (shrink)

Dai saggi raccolti in questo volume da Garin emergono le linee di una storia della civiltà del Rinascimento italiano. Lo studio dello stretto intreccio tra vita intellettuale e vita politica, soprattutto nella Firenze fra Tre e Quattrocento, costituisce il punto di partenza per una nuova interpretazione di questo periodo. Le origini dell'Umanesimo vanno cercate nel rapporto fra la tradizione di libertà e democrazia della repubblica fiorentina e l'immagine ideale della repubblica come erede di Roma.

Sulla dignità umana -- Bioetica senza fondamento? -- Una sovranità limitata per la ricerca scientifica: ossimoro o truismo -- Ius quia iussum e ius quia iustum (considerazioni su alcuni passi del libro della genesi) -- La pace come problema -- A proposito di religioni, identità nazionali e diritto -- Su costituzioni e costituzionalismo -- A proposito del trattato politico di Spinoza -- A proposito dei lineamenti fondamentali di filosofia del diritto di Hegel -- A proposito degli elementi di scienza politica (...) di Mosca -- Su Michels -- Su luigi einaudi 'italiano del tutto particolare' -- Guerra e pace secondo cotta -- Una postilla non scientifica (ovvero: un dittico contro Schmitt). (shrink)

1. Le fe por la palabra -- 2. Topía y Utopía -- 3. Luz en la caverna.

v. 1. Proceedings, Rome, 2001-2004 -- v. 2. Giornate di studi, 2005-2008.

This volume illustrates to the public, and legal experts, the basic principles of the field of neuroscience, that commonly goes under the name of Neurolaw. First, it illustrates the relationship between neuroscience, natural sciences and social sciences. Furthermore, it highlights numerous problems concerning the fundamental philosophical concepts used by Neurolaw and evaluates the validity of the method and the limits of a neuroscientific approach to the problems of law and justice. The volume explores the possibility of application of these concepts (...) on the fundamentals of the general theory of law and legal dogmatics. It also examines the main problems of Neurolaw in relation to public, private, criminal and procedural law. In conclusion, the book follows a systematic method that makes it an thorough manual for the introduction to Neurolaw. (shrink)

Partial proceedings of the 17th World Congress, International Association for Philosophy of Law and Social Philosophy, Bologna, 1995.