Non-deterministic algebraization of logics by swap structures1

Multialgebras have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap structures are given. Specifically, a formal study of swap structures for LFIs is developed, by adapting concepts of universal algebra to multialgebras in a suitable way. A decomposition theorem similar to Birkhoff’s representation theorem is obtained for each class of swap structures. Moreover, when applied to the 3-valued algebraizable logics J3 and Ciore, their classes of algebraic models are retrieved, and the swap structures semantics become twist structures semantics. This fact, together with the existence of a functor from the category of Boolean algebras to the category of swap structures for each LFI, suggests that swap structures can be seen as non-deterministic twist structures. This opens new avenues for dealing with non-algebraizable logics by the more general methodology of multialgebraic semantics

Normal Proofs and Tableaux for the Font-Rius Tetravalent Modal Logic

Tetravalent modal logic (TML) was introduced by Font and Rius in 2000. It is an expansion of the Belnap-Dunn four-valued logic FOUR, a logical system that is well-known for the many applications found in several fields. Besides, TML is the logic that preserves degrees of truth with respect to Monteiro’s tetravalent modal algebras. Among other things, Font and Rius showed that TML has a strongly adequate sequent system, but unfortunately this system does not enjoy the cut-elimination property. However, in a previous work we presented a sequent system for TML with the cut-elimination property. Besides, in this same work, it was also presented a sound and complete natural deduction system for this logic. In the present article we continue with the study of TML under a proof-theoretic perspective. In the first place, we show that the natural deduction system that we introduced before admits a normalization theorem. In the second place, taking advantage of the contrapositive implication for the tetravalent modal algebras introduced by A. V. Figallo and P. Landini, we define a decidable tableau system adequate to check validity in the logic TML. Finally, we provide a sound and complete tableau system for TML in the original language. These two tableau systems constitute new (proof-theoretic) decision procedures for checking validity in the variety of tetravalent modal algebras

First-order swap structures semantics for some Logics of Formal Inconsistency

The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (that is, logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special class of multialgebras. The proposed semantical framework generalizes previous aproaches to quantified LFIs presented in the literature. The case of QmbC, the simpler quantified LFI expanding classical logic, will be analyzed in detail. An axiomatic extension of QmbC called QLFI1o is also studied, which is equivalent to the quantified version of da Costa and D'Ottaviano 3-valued logic J3. The semantical structures for this logic turn out to be Tarkian structures based on twist structures. The expansion of QmbC and QLFI1o with a standard equality predicate is also considered

G'3 as the logic of modal 3-valued Heyting algebras

In 2001, W. Carnielli and Marcos considered a 3-valued logic in order to prove that the schema ϕ ∨ (ϕ → ψ) is not a theorem of da Costa’s logic Cω. In 2006, this logic was studied (and baptized) as G'3 by Osorio et al. as a tool to define semantics of logic programming. It is known that the truth-tables of G'3 have the same expressive power than the one of Łukasiewicz 3-valued logic as well as the one of Gödel 3-valued logic G3. From this, the three logics coincide up-to language, taking into acccount that 1 is the only designated truth-value in these logics. From the algebraic point of view, Canals-Frau and Figallo have studied the 3-valued modal implicative semilattices, where the modal operator is the well-known Moisil-Monteiro-Baaz Δ operator, and the supremum is definable from this. We prove that the subvariety obtained from this by adding a bottom element 0 is term-equivalent to the variety generated by the 3-valued algebra of G'3. The algebras of that variety are called G'3-algebras. From this result, we obtain the equations which axiomatize the variety of G'3-algebras. Moreover, we prove that this variety is semisimple, and the 3-element and the 2-element chains are the unique simple algebras of the variety. Finally an extension of G'3 to first-order languages is presented, with an algebraic semantics based on complete G'3-algebras. The corresponding soundness and completeness theorems are obtained

Kissing molars extraction: case series and review of the literature

Kissing molars are a very rare form of inclusion defined as molars included in the same quadrant, with occlusal surfaces contacting each other within a single dental follicle. We present four cases of this pathology: a 35 year-old male, referred to the Oral and Maxillofacial Surgery Department of the Hospital Virgen del Rocio in Seville, and three females of 24, 26, and 31 years, all of which had kissing molars that were treated by tooth extraction. We have found only 10 cases published in the medical literature in which this type of inclusion is briefly described, none of which elaborate on the surgical technique employed. In these cases, the indication for surgery is established when there is a history of recurring infections or cystic lesions associated with dental inclusions. The extraction of kissing molars requires an exhaustive comprehension of the anatomy of the region involved, sufficiently developed surgical abilities, and an extensive planning proces

Relationship Between Osteoporosis and Marginal Bone Loss in Osseointegrated Implants: A 2-Year Retrospective Study

Background: Fitting implants in osteoporotic patients has raditionally been controversial, and there is little scientific evidence relating osteoporosis to marginal bone loss (MBL). The aims of this study are as follows: 1) to evaluate the possibility of a correlation between osteoporosis, as measured by the mandibular cortical index (MCI), and MBL and 2) to assess how various systemic diseases, periodontitis, and placement of implants in regenerated bone are correlated with MBL and MCI. Methods: This retrospective study examines 212 implants inserted in 67 patients. To take a possible cluster failure into account, an implant for each patient was selected (n = 67 implants). MBL was assessed. Osteoporosis was evaluated using the MCI. Both MBL and MCI were assessed from panoramic radiographs. x2 test was performed (Haberman post hoc test). Significance was P <0.05. Results: When the total sample implant (N = 212) was evaluated, a significant association was found between the presence of osteoporosis and MCI (P <0.001) and between the presence of diabetes mellitus and MCI (P <0.01). Significant associations were also found between MBL and placement of implants in regenerated sites (P <0.001) and between MBL and a previous history of periodontitis (P <0.05). When the sample is evaluated only in selected implants (one per patient, n = 67), significant differences appear to relate only to the MBL with the placement of implants in regenerated bone sites (P <0.001). Conclusions: Osteoporosis (as evaluated by MCI) does not pose a risk for the development of greater MBL. Parameters adversely affecting the development of increased MBL are a previous history of periodontitis and especially the placement of implants at sites of bone regeneration

High-Density Microwell Chip for Culture and Analysis of Stem Cells

With recent findings on the role of reprogramming factors on stem cells, in vitro screening assays for studying (de)-differentiation is of great interest. We developed a miniaturized stem cell screening chip that is easily accessible and provides means of rapidly studying thousands of individual stem/progenitor cell samples, using low reagent volumes. For example, screening of 700,000 substances would take less than two days, using this platform combined with a conventional bio-imaging system. The microwell chip has standard slide format and consists of 672 wells in total. Each well holds 500 nl, a volume small enough to drastically decrease reagent costs but large enough to allow utilization of standard laboratory equipment. Results presented here include weeklong culturing and differentiation assays of mouse embryonic stem cells, mouse adult neural stem cells, and human embryonic stem cells. The possibility to either maintain the cells as stem/progenitor cells or to study cell differentiation of stem/progenitor cells over time is demonstrated. Clonality is critical for stem cell research, and was accomplished in the microwell chips by isolation and clonal analysis of single mouse embryonic stem cells using flow cytometric cell-sorting. Protocols for practical handling of the microwell chips are presented, describing a rapid and user-friendly method for the simultaneous study of thousands of stem cell cultures in small microwells. This microwell chip has high potential for a wide range of applications, for example directed differentiation assays and screening of reprogramming factors, opening up considerable opportunities in the stem cell field

The incidence of unpleasant dreams after sub-anaesthetic ketamine

Ketamine is an N-methyl-D-aspartate (NMDA)receptor antagonist with psychotogenic effects and for whichthere are diverse reports of whether pleasant or unpleasantdreams result during anaesthesia, post-operatively or aftersub-anaesthetic use. The aim was to assess in healthy volunteers the incidence ofunpleasant dreams over the three nights after receiving asub-anaesthetic dose of ketamine, in comparison to placebo,and with retrospective home nightmare frequency as acovariate.Thirty healthy volunteers completed questionnairesabout retrospective home dream recall and were then giveneither ketamine or placebo. Ketamine resulted in significantly more meandream unpleasantness relative to placebo and caused athreefold increase in the odds ratio for the incidence of anunpleasant dream. The number of dreams reported over thethree nights did not differ between the groups. Theincidence of unpleasant dreams after ketamine use waspredicted by retrospectively assessed nightmare frequencyat home.Ketamine causes unpleasant dreams over thethree post-administration nights. This may be evidence of aresidual psychotogenic effect that is not found on standardself-report symptomatology measures or a result of disturbedsleep electrophysiology. The results have theoretical implications for the relationship between nightmares and schizotypy

Bioreactors as engineering support to treat cardiac muscle and vascular disease

Cardiovascular disease is the leading cause of morbidity and mortality in the Western World. The inability of fully differentiated, load-bearing cardiovascular tissues to in vivo regenerate and the limitations of the current treatment therapies greatly motivate the efforts of cardiovascular tissue engineering to become an effective clinical strategy for injured heart and vessels. For the effective production of organized and functional cardiovascular engineered constructs in vitro, a suitable dynamic environment is essential, and can be achieved and maintained within bioreactors. Bioreactors are technological devices that, while monitoring and controlling the culture environment and stimulating the construct, attempt to mimic the physiological milieu. In this study, a review of the current state of the art of bioreactor solutions for cardiovascular tissue engineering is presented, with emphasis on bioreactors and biophysical stimuli adopted for investigating the mechanisms influencing cardiovascular tissue development, and for eventually generating suitable cardiovascular tissue replacements