Categorical Abstract Logic: Hidden Multi-Sorted Logics as Multi-Term Institutions

Babenyshev and Martins proved that two hidden multi-sorted deductive systems are deductively equivalent if and only if there exists an isomorphism between their corresponding lattices of theories that commutes with substitutions. We show that the -institutions corresponding to the hidden multi-sorted deductive systems studied by Babenyshev and Martins satisfy the multi-term condition of Gil-Férez. This provides a proof of the result of Babenyshev and Martins by appealing to the general result of Gil-Férez pertaining to arbitrary multi-term -institutions. The approach places hidden multi-sorted deductive systems in a more general framework and bypasses the laborious reuse of well-known proof techniques from traditional abstract algebraic logic by using “off the shelf” tools

Categorical Abstract Algebraic Logic: Referential π-Institutions

Wójcicki introduced in the late 1970s the concept of a referential semantics for propositional logics. Referential semantics incorporate features of the Kripke possible world semantics for modal logics into the realm of algebraic and matrix semantics of arbitrary sentential logics. A well-known theorem of Wójcicki asserts that a logic has a referential semantics if and only if it is selfextensional. Referential semantics was subsequently studied in detail by Malinowski and the concept of selfextensionality has played, more recently, an important role in the field of abstract algebraic logic in connection with the operator approach to algebraizability. We introduce and review some of the basic definitions and results pertaining to the referential semantics of π-institutions, abstracting corresponding results from the realm of propositional logics

Categorical Abstract Algebraic Logic: Equivalence of Closure Systems

In their famous ``Memoirs monograph, Blok and Pigozzi defined algebraizable deductive systems as those whose consequence relation is equivalent to the algebraic consequence relation associated with a quasivariety of universal algebras. In characterizing this property, they showed that it is equivalent with the existence of an isomorphism between the lattices of theories of the two consequence relations that commutes with inverse substitutions. Thus emerged the prototypical and paradigmatic result relating an equivalence between two consequence relations established by means of syntactic translations and the isomorphism between corresponding lattices of theories. This result was subsequently generalized in various directions. Blok and Pigozzi themselves extended it to cover equivalences between $k$-deductive systems. Rebagliato and Verd\\u27{u} and, later, also Pynko and Raftery, considered equivalences between consequence relations on associative sequents. The author showed that it holds for equivalences between two term $\pi$-institutions. Blok and J\\u27{o}nsson considered equivalences between structural closure operations on regular $M$-sets. Gil-F\\u27{e}rez lifted the author\u27s results to the case of multi-term $\pi$-institutions. Finally, Galatos and Tsinakis considered the case of equivalences between closure operators on ${\bf A}$-modules and provided an exact characterization of those that are induced by syntactic translations. In this paper, we contribute to this line of research by further abstracting the results of Galatos and Tsinakis to the case of consequence systems on ${\bf Sign}$-module systems, which are set-valued functors \SEN:{\bf Sign}\ra{\bf Set} on complete residuated categories ${\bf Sign}$

Epithelial to mesenchymal transition in the pathogenesis of uterine malignant mixed Müllerian tumours: the role of ubiquitin proteasome system and therapeutic opportunities

Malignant mixed Müllerian tumours (malignant mixed mesodermal tumours, MMMT) of the uterus are metaplastic carcinomas with a sarcomatous component and thus they are also called carcinosarcomas. It has now been accepted that the sarcomatous component is derived from epithelial elements that have undergone metaplasia. The process that produces this metaplasia is epithelial to mesenchymal transition (EMT), which has recently been described as a neoplasia-associated programme shared with embryonic development and enabling neoplastic cells to move and metastasise. The ubiquitin proteasome system (UPS) regulates the turnover and functions of hundreds of cellular proteins. It plays important roles in EMT by being involved in the regulation of several pathways participating in the execution of this metastasis-associated programme. In this review the specific role of UPS in EMT of MMMT is discussed and therapeutic opportunities from UPS manipulations are propose

Federated description logics for the semantic web

The thesis deals with a family of federated description logics for creating modular ontologies in the semantic web. All these logics share modularity, the possibility to reuse concept names and role names by importing, and context-sensitive interpretation of all logical connectives. Apart from the main basic language F-ALCI, we present a lattice-based extension LF-ALCI, a probabilistic extension PF-ALCI and an extension that employs knowledge operators F-ALCIK. All languages are based on the ordinary well-known description logic ALCI

Categorical Abstract Algebraic Logic: Equivalential π-Institutions

The theory of equivalential deductive systems, as introduced by Prucnal and Wroński and further developed by Czelakowski, is abstracted to cover the case of logical systems formalized as π-Institutions. More precisely, the notion of an N-equivalence system for a given π-Institutions is introduced. A characterization theorem for N-equivalence systems, previously proven for N-parameterized equivalence systems, is revisited and a “transfer theorem” for N-equivalence systems is proven. For a π-Institutions I having an N-equivalence system, the maximum such system is singled out and, then, an analog of Herrmann’s Test, characterizing those N-protoalgebraic π-Institutions having an N-equivalence system, is formulated. Finally, some of the rudiments of matrix theory are revisited in the context of π-Institutions, as they relate to the existence of N-equivalence systems

Ubiquitin- and ubiquitin-like proteins-conjugating enzymes (E2s) in breast cancer

Breast cancer is the most common malignancy in women and a significant cause of morbidity and mortality. Sub-types of breast cancer defined by the expression of steroid hormones and Her2/Neu oncogene have distinct prognosis and undergo different therapies. Besides differing in their phenotype, sub-types of breast cancer display various molecular lesions that participate in their pathogenesis. BRCA1 is one of the common hereditary cancer predisposition genes and encodes for an ubiquitin ligase. Ubiquitin ligases or E3 enzymes participate together with ubiquitin activating enzyme and ubiquitin conjugating enzymes in the attachment of ubiquitin (ubiquitination) in target proteins. Ubiquitination is a post-translational modification regulating multiple cell functions. It also plays important roles in carcinogenesis in general and in breast carcinogenesis in particular. Ubiquitin conjugating enzymes are a central component of the ubiquitination machinery and are often perturbed in breast cancer. This paper will discuss ubiquitin and ubiquitin-like proteins conjugating enzymes participating in breast cancer pathogenesis, their relationships with other proteins of the ubiquitination machinery and their role in phenotype of breast cancer sub-type

Categorical abstract algebraic logic

In (1) * the theory of algebraizable deductive systems was developed. A deductive system S over a language L is said to be algebraizable if there exists a quasi-variety K, over the same language L, and translations from the sentences of the system into equations and vice-versa that, roughly speaking, simulate the deduction over the system in the equational deduction over the quasi-variety and vice-versa and are inverses of each other. In (3) this notion of algebraizability was shown to be a special case of the, so-called, equivalence of deductive systems. It is, in fact, the equivalence of S with the very special 2-deductive system (2) associated with the quasi-variety K;One of the main limitations of this framework is the way in which it handles logics with varying signatures, like equational or first-order logic. Before they can be algebraized in this framework, they must be transformed in a rather artificial way to propositional-like structural counterparts;In this thesis, following (4), the [pi]-institution framework (5, 6, 7) is used to extend the theory of algebraizability to logics with varying signatures. The notion of equivalence for [pi]-institutions is introduced. A characterization of equivalence for a special class of [pi]-institutions, the, so-called, term [pi]-institutions, is obtained along the lines of (2), by exploiting the relation between their categories of theories. The notion of an algebraic institution is then defined. Algebraic institutions roughly correspond to equational 2-deductive systems, but the formalism here is categorical rather than universal algebraic so that it can handle the added generality appropriately. These special institutions are used for the algebraization of arbitrary [pi]-institutions. The example of the equational institution illustrates the general theory. Limiting the scope to a subclass of term [pi]-institutions, the, so-called, theory institutions, and requiring the syntax to remain invariant during the algebraization process, an intrinsic characterization is obtained for algebraizability in the spirit of (1), via the introduction of a generalized Leibniz operator. The study of the invariance of some metalogical properties under equivalence of [pi]-institutions and the detailed development of the algebraic theory used in the algebraization of the equational institution conclude the thesis. ftn*Please refer to dissertation for references

The ubiquitin-proteasome system and signal transduction pathways regulating Epithelial Mesenchymal transition of cancer.

Epithelial to Mesenchymal transition (EMT) in cancer, a process permitting cancer cells to become mobile and metastatic, has a signaling hardwire forged from development. Multiple signaling pathways that regulate carcinogenesis enabling characteristics in neoplastic cells such as proliferation, resistance to apoptosis and angiogenesis are also the main players in EMT. These pathways, as almost all cellular processes, are in their turn regulated by ubiquitination and the Ubiquitin-Proteasome System (UPS). Ubiquitination is the covalent link of target proteins with the small protein ubiquitin and serves as a signal to target protein degradation by the proteasome or to other outcomes such as endocytosis, degradation by the lysosome or specification of cellular localization. This paper reviews signal transduction pathways regulating EMT and being regulated by ubiquitination

Categorical Abstract Algebraic Logic: Equivalential π-Institutions

The theory of equivalential deductive systems, as introduced by Prucnal and Wroński and further developed by Czelakowski, is abstracted to cover the case of logical systems formalized as π-Institutions. More precisely, the notion of an N-equivalence system for a given π-Institutions is introduced. A characterization theorem for N-equivalence systems, previously proven for N-parameterized equivalence systems, is revisited and a “transfer theorem” for N-equivalence systems is proven. For a π-Institutions I having an N-equivalence system, the maximum such system is singled out and, then, an analog of Herrmann’s Test, characterizing those N-protoalgebraic π-Institutions having an N-equivalence system, is formulated. Finally, some of the rudiments of matrix theory are revisited in the context of π-Institutions, as they relate to the existence of N-equivalence systems