An algebraic investigation of Linear Logic

In this paper we investigate two logics from an algebraic point of view. The two logics are: MALL (multiplicative-additive Linear Logic) and LL (classical Linear Logic). Both logics turn out to be strongly algebraizable in the sense of Blok and Pigozzi and their equivalent algebraic semantics are, respectively, the variety of Girard algebras and the variety of girales. We show that any variety of girales has equationally definable principale congruences and we classify all varieties of Girard algebras having this property. Also we investigate the structure of the algebras in question, thus obtaining a representation theorem for Girard algebras and girales. We also prove that congruence lattices of girales are really congruence lattices of Heyting algebras and we construct examples in order to show that the variety of girales contains infinitely many nonisomorphic finite simple algebras

Why most papers on filters are really trivial (including this one)

The aim of this note is to show that many papers on various kinds of filters (and related concepts) in (subreducts of) residuated structures are in fact easy consequences of more general results that have been known for a long time

Projectivity in (bounded) integral residuated lattices

In this paper we study projective algebras in varieties of (bounded) commutative integral residuated lattices from an algebraic (as opposed to categorical) point of view. In particular we use a well-established construction in residuated lattices: the ordinal sum. Its interaction with divisibility makes our results have a better scope in varieties of divisibile commutative integral residuated lattices, and it allows us to show that many such varieties have the property that every finitely presented algebra is projective. In particular, we obtain results on (Stonean) Heyting algebras, certain varieties of hoops, and product algebras. Moreover, we study varieties with a Boolean retraction term, showing for instance that in a variety with a Boolean retraction term all finite Boolean algebras are projective. Finally, we connect our results with the theory of Unification

Structural and universal completeness in algebra and logic

In this work we study the notions of structural and universal completeness both from the algebraic and logical point of view. In particular, we provide new algebraic characterizations of quasivarieties that are actively and passively universally complete, and passively structurally complete. We apply these general results to varieties of bounded lattices and to quasivarieties related to substructural logics. In particular we show that a substructural logic satisfying weakening is passively structurally complete if and only if every classical contradiction is explosive in it. Moreover, we fully characterize the passively structurally complete varieties of MTL-algebras, i.e., bounded commutative integral residuated lattices generated by chains.Comment: This is a preprin

The educational value, both past and present, of an ancient scientific collection: the collection of anatomical preparations illustrating the various phases of bone development, from the second month of intrauterine life to adulthood

Italy’s museums possess an enormous patrimony of historical scientific artefacts. This raises important questions regarding the conservation and safeguard of such materials and prompts reflection as to the utility of current modalities of popularising science. The collections housed in scientific museums were created in order to promote scientific education by making science more accessible and more comprehensible. The authors ask whether this heritage can still be used for educational purposes today, and examine a collection of preparations on the ossification of human bones in the Anatomical Museum of the University of Siena. They conclude that such materials can still be of educational value if they are made part of exhibitions that meet the needs of the public and of students in training. Indeed, it is essential to bear witness to the long pathway of the development of scientific knowledge and, in particular, to the value of the research on which this knowledge is based. Through the implementation of ad hoc exhibitions, this precious historical scientific patrimony can continue to play an important role in presenting medical/healthcare issues of topical interest without losing sight of the relevance of past experience to basic teaching

On Freese's technique

In this paper we explore some applications of a certain technique (that we call the Freese's technique), which is a tool for identifying certain lattices as sublattices of the congruence lattice of a given algebra. In particular we will give sufficient conditions for two family of lattices (called the rods and the snakes) to be admissible as sublattices of a variety generated by a given algebra, extending an unpublished result of R. Freese and P. Lipparini

AN ABNORMALLY LONG STYLOID PROCESS WITH OSSIFICATION OF THE STYLOHYOID LIGAMENT

The styloid process of the temporal bone is an elongated bony projection presenting a variable length as demonstrated in osteometric and radiological studies conducted with different techniques: three-dimensional computed tomography (3dct) or dental panoramic three-dimensional scanning. An elongated styloid process can cause neck pain , dysphagia, headache, sore throat, ear pain, mandibular dysfunction which characterize Eagle’s syndrome. Here we present a rare image of an abnormally long styloid process with ossification of left stylohyoid ligament belonging to a bone collection of the local anatomical museum , part of our department, and discovered during routine osteology classes .Also if a direct relation between the length of the styloid process and syndrome of Eagle is not always obvious ,radiologists , neurologists,neurosurgeons, dentists, anesthetists and otolaryngologists could be aware of this bone anomaly to diagnose this syndrome