Epistemic modals have peculiar logical features that are challenging to account for in a broadly classical framework. For instance, while a sentence of the form $$p\wedge \Diamond \lnot p$$ (‘p, but it might be that not p’) appears to be a contradiction, $$\Diamond \lnot p$$ does not entail $$\lnot p$$, which would follow in classical logic. Likewise, the classical laws of distributivity and disjunctive syllogism fail for epistemic modals. Existing attempts to account for these facts generally either under- or over-correct. (...) Some theories predict that $$ p\wedge \Diamond \lnot p$$, a so-called epistemic contradiction, is a contradiction only in an etiolated sense, under a notion of entailment that does not always allow us to replace $$p\wedge \Diamond \lnot p$$ with a contradiction; these theories underpredict the infelicity of embedded epistemic contradictions. Other theories savage classical logic, eliminating not just rules that intuitively fail, like distributivity and disjunctive syllogism, but also rules like non-contradiction, excluded middle, De Morgan’s laws, and disjunction introduction, which intuitively remain valid for epistemic modals. In this paper, we aim for a middle ground, developing a semantics and logic for epistemic modals that makes epistemic contradictions genuine contradictions and that invalidates distributivity and disjunctive syllogism but that otherwise preserves classical laws that intuitively remain valid. We start with an algebraic semantics, based on ortholattices instead of Boolean algebras, and then propose a possibility semantics, based on partial possibilities related by compatibility. Both semantics yield the same consequence relation, which we axiomatize. We then show how to lift an arbitrary possible worlds model for a non-modal language to a possibility model for a language with epistemic modals. The goal throughout is to retain what is desirable about classical logic while accounting for the non-classicality of epistemic vocabulary. (shrink)

Orthologic is non-classical logic and has been studied as a part of quantumlogic. OL is based on an ortholattice and is also called minimal quantum logic. Sequent calculus is used as a tool for proof in logic and has been examinedfor several decades. Although there are many studies on sequent calculus forOL, these sequent calculi have some problems. In particular, they do not includeimplication connective and they are mostly incompatible with the cut-eliminationtheorem. In this paper, we introduce new labeled sequent (...) calculus called LGOI, and show that this sequent calculus solve the above problems. It is alreadyknown that OL is decidable. We prove that decidability is preserved when theimplication connective is added to OL. (shrink)

In this paper, we present three main results on orthologics. Firstly, we give a sufficient condition for an orthologic to have variable separation property and show that the orthomodular logic has this property. Secondly, we show that the class of modular orthologics has an infinite descending chain. Finally we show that there exists a continuum of orthologics.

Recently, we (Synthese, 199(5–6):13247–13281, 2021) proposed Kripke-like semantics for two quantum logics of interderminacy. These logics expand the vocabulary of standard Birkhoff-von Neumann propositional quantum logic with a pair of modal operators interpreted as “it is (in)determinate that”, allowing them to express in the object language statements such as “it is indeterminate that system S is spin-up in the x-direction”, as well as statements of any logical complexity involving ascriptions of (in)determinacy. We present an axiomatization of a logic closely related (...) to one of these quantum logics of indeterminacy and prove that this axiomatization is sound and complete with respect to the Kripke-like semantics. We then prove that this logic is decidable. (shrink)

In the present paper we give the first proof-theoretical example of an embedding of classical logic into a quantum-like logic. This is performed in the framework of basic logic, where a proof-theoretical approach to quantum logic is convenient. We consider basic orthologic, that corresponds to a sequential formulation of paraconsistent quantum logic, and which is given by basic orthologic added with weakening and contraction, in a language with Girard's negation. In the paper we first consider a convenient cut-free calculus for (...) classical logic, in the same language; then, in a language enriched with a new kind of literals, we introduce basic orthologic with a primitive modality, where classical logic is embeddable. Similarly to Girard's negation, our modality is not a connective but conceivable as an operator defined inductively on the set of formulae. This allows us to obtain a calculus which enjoys cut-elimination. (shrink)

In this paper, we consider three different search strategies for a cut-free sequent system formalizing orthologic, and estimate the respective search spaces. Applying backward search, there are classes of formulae for which both the minimal proof length and the search space are exponential. In a combined forward and backward approach, all proofs are polynomial, but the potential search space remains exponential. Using a forward strategy, the potential search space becomes polynomial yielding a polynomial decision procedure for orthologic and the word (...) problem for free ortholattices. (shrink)

In this study, new sequent calculi for a minimal quantum logic ) are discussed that involve an implication. The sequent calculus \ for \ was established by Nishimura, and it is complete with respect to ortho-models. As \ does not contain implications, this study adopts the strict implication and constructs two new sequent calculi \ and \ as the expansions of \. Both \ and \ are complete with respect to the O-models. In this study, the completeness and decidability theorems (...) for these new systems are proven. Furthermore, some details pertaining to new rules and the strict implication are discussed. (shrink)

We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present a Fitch-style natural deduction system for the logic that contains only the introduction and elimination rules for the logical constants. From this starting point, if one adds the rule that Fitch called Reiteration, one obtains a proof system for intuitionistic logic in the given signature; (...) if instead of adding Reiteration, one adds the rule of Reductio ad Absurdum, one obtains a proof system for orthologic; by adding both Reiteration and Reductio, one obtains a proof system for classical logic. Arguably neither Reiteration nor Reductio is as intimately related to the meaning of the connectives as the introduction and elimination rules are, so the base logic we identify serves as a more fundamental starting point and common ground between proponents of intuitionistic logic, orthologic, and classical logic. The algebraic semantics for the logic we motivate proof-theoretically is based on bounded lattices equipped with what has been called a weak pseudocomplementation. We show that such lattice expansions are representable using a set together with a reflexive binary relation satisfying a simple first-order condition, which yields an elegant relational semantics for the logic. This builds on our previous study of representations of lattices with negations, which we extend and specialize for several types of negation in addition to weak pseudocomplementation; in an appendix, we further extend this representation to lattices with implications. Finally, we discuss adding to our logic a conditional obeying only introduction and elimination rules, interpreted as a modality using a family of accessibility relations. (shrink)

Challenges to classical logic have emerged from several sources. According to recent work, the behavior of epistemic modals in natural language motivates weakening classical logic to orthologic, a logic originally discovered by Birkhoff and von Neumann in the study of quantum mechanics. In this paper, we consider a different tradition of thinking that the behavior of vague predicates in natural language motivates weakening classical logic to intuitionistic logic or even giving up some intuitionistic principles. We focus in particular on Fine's (...) recent approach to vagueness. Our main question is: what is a natural non-classical base logic to which to retreat in light of both the non-classicality emerging from epistemic modals and the non-classicality emerging from vagueness? We first consider whether orthologic itself might be the answer. We then discuss whether accommodating the non-classicality emerging from epistemic modals and vagueness might point in the direction of a weaker system of fundamental logic. (shrink)

In this paper, we study three representations of lattices by means of a set with a binary relation of compatibility in the tradition of Ploščica. The standard representations of complete ortholattices and complete perfect Heyting algebras drop out as special cases of the first representation, while the second covers arbitrary complete lattices, as well as complete lattices equipped with a negation we call a protocomplementation. The third topological representation is a variant of that of Craig, Haviar, and Priestley. We then (...) extend each of the three representations to lattices with a multiplicative unary modality; the representing structures, like so-called graph-based frames, add a second relation of accessibility interacting with compatibility. The three representations generalize possibility semantics for classical modal logics to non-classical modal logics, motivated by a recent application of modal orthologic to natural language semantics. (shrink)

We developed an ex silico evolutionary‐based systematic synteny approach to define and name the duplicated genes in vertebrates. The first convention for the naming of genes relied on historical precedent, the order in the human genome, and mutant phenotypes in model systems. However, total‐genome duplication that resulted in teleost genomes required the naming of duplicated orthologous genes (ohnologs) in a specific manner. Unfortunately, as we review here, such naming has no defined criteria, and some ohnologs and their orthologs have (...) suffered from incorrect nomenclature, thus creating confusion in comparative genetics and disease modeling. We sought to overcome this barrier by establishing an ex silico evolutionary‐based systematic approach to naming ohnologs in teleosts. We developed software and compared gene synteny in zebrafish using the spotted gar genome as a reference, representing the unduplicated ancestral state. Using new criteria, we identified several hundred potentially misnamed ohnologs and validated the principle manually. Also see the video abstract here: https://youtu.be/UKNLa_TvSgY. (shrink)

Orthologic is defined by weakening the axioms and rules of inference of the classical propositional calculus. The resulting Lindenbaum-Tarski quotient algebra is an orthoimplication algebra which generalizes the author's implication algebra. The associated order structure is a semi-orthomodular lattice. The theory of orthomodular lattices is obtained by adjoining a falsity symbol to the underlying orthologic or a least element to the orthoimplication algebra.

Comparing expression patterns of orthologous genes between insects and vertebrates, we have recently proposed that the ventral nerve cord in insects may correspond to the dorsal nerve cord in vertebrates. Here we show that the early development of the insect and vertebrate brain anlagen is indeed very similar. Insect and vertebrate brains express similar sets of genes in comparable areas with similar functions in the adult. In addition, early axogenesis establishes surprisingly similar patterns of axonal connectivity in both groups. We (...) therefore propose that insect and vertebrate brains are built according to a common ground plan, and that specific areas of the insect and vertebrate brains be considered as homologous, meaning that these areas already existed, with their specific functions, in their common ancestor. (shrink)

Some algebraic structures of the set of all effects are investigated and summarized in the notion of a(weak) orthoalgebra. It is shown that these structures can be embedded in a natural way in lattices, via the so-calledMacNeille completion. These structures serve as a model ofparaconsistent quantum logic, orthologic, andorthomodular quantum logic.

This paper is a study of similarities and differences between strong and weak quantum consequence operations determined by a given class of ortholattices. We prove that the only strong orthologics which admits the deduction theorem (the only strong orthologics with algebraic semantics, the only equivalential strong orthologics, respectively) is the classical logic.

The reconstruction of bacterial evolutionary relationships has proven to be a daunting task because variable mutation rates and horizontal gene transfer (HGT) among species can cause grave incongruities between phylogenetic trees based on single genes. Recently, a highly robust phylogenetic tree was constructed for 13 γ‐proteobacteria using the combined alignments of 205 conserved orthologous proteins.1 Only two proteins had incongruent tree topologies, which were attributed to HGT between Pseudomonas species and Vibrio cholerae or enterics. While the evolutionary relationships among these (...) species appears to be resolved, further analysis suggests that HGT events with other bacterial partners likely occurred; this alters the implicit assumption of γ‐proteobacteria monophyly. Thus, any thorough reconstruction of bacterial evolution must not only choose a suitable set of molecular markers but also strive to reduce potential bias in the selection of species. BioEssays 26:463–468, 2004. © 2004 Wiley Periodicals, Inc. (shrink)

Antibiotic resistance in bacteria has become a great threat to global public health. Tigecycline is a next‐generation tetracycline that is the final line of defense against severe infections by pan‐drug‐resistant bacterial pathogens. Unfortunately, this last‐resort antibiotic has been challenged by the recent emergence of the mobile Tet(X) orthologs that can confer high‐level tigecycline resistance. As it is reviewed here, these novel tetracycline destructases represent a growing threat to the next‐generation tetracyclines, and a basic framework for understanding the molecular epidemiology (...) and resistance mechanisms of them is presented. However, further large‐scale epidemiological and functional studies are urgently needed to better understand the prevalence and dissemination of these newly discovered Tet(X) orthologs among Gram‐negative bacteria in both human and veterinary medicine. (shrink)

The functions of the Bloom syndrome helicase and its orthologs are well characterized in mitotic DNA damage repair, but their roles within the context of meiotic recombination are less clear. In meiotic recombination, multiple repair pathways are used to repair meiotic DSBs, and current studies suggest that BLM may regulate the use of these pathways. Based on literature from Saccharomyces cerevisiae, Arabidopsis thaliana, Mus musculus, Drosophila melanogaster, and Caenorhabditis elegans, we present a unified model for a critical meiotic role (...) of BLM and its orthologs. In this model, BLM and its orthologs utilize helicase activity to regulate the use of various pathways in meiotic recombination by continuously disassembling recombination intermediates. This unwinding activity provides the meiotic program with a steady pool of early recombination substrates, increasing the probability for a DSB to be processed by the appropriate pathway. As a result of BLM activity, crossovers are properly placed throughout the genome, promoting proper chromosomal disjunction at the end of meiosis. This unified model can be used to further refine the complex role of BLM and its orthologs in meiotic recombination. In meiotic recombination, Blm utilizes its helicase activity to disassemble early recombination intermediates, thereby retaining a pool of recombination sites from which some can be selected to enter the Class I crossover pathway while simultaneously promoting SDSA and preventing the use of the Class II pathway. (shrink)

Heterotrimeric G proteins, consisting of α, β, and γ subunits, couple ligand-bound seven transmembrane domain receptors to the regulation of effector proteins and production of intracellular second messengers. G protein signaling mediates the perception of environmental cues in all higher eukaryotic organisms, including yeast, Dictyostelium, plants, and animals. The nematode Caenorhabditis elegans is the first animal to have complete descriptions of its cellular anatomy, cell lineage, neuronal wiring diagram, and genomic sequence. In a recent paper, Jansen et al.(1) used sequence (...) searches of the C. elegans genome database to identify all heterotrimeric G protein genes (20 Gα, 2 Gβ, 2 Gγ). C. elegans encodes one ortholog of each of the four Gα classes found in metazoans and 16 new Gα genes. The orthologous genes are widely expressed, whereas 14 of the divergent Gα genes are almost exclusively expressed in sensory neurons where they may regulate perception and chemotaxis.BioEssays 21:713–717, 1999. © 1999 John Wiley & Sons, Inc. (shrink)

The evolutionary origins of several vertebrate organs are still controversial. The thyroid is classically thought to derive directly from the endostyle (a pharyngeal organ found in urochordates, cephalochordates and lampreys). Several molecular and biochemical lines of evidence agree with this scenario. However, a recent paper,1 describing the expression of a FoxE ortholog in amphioxus, suggests that some molecular pathways might actually have been recruited from an adjacent region of the pharynx. Although additional data from urochordates and lamprey are needed to (...) confirm this hypothesis; these results propose an interesting new scenario for thyroid evolution that involved the reorganisation of genetical and morphological features in the pharyngeal endoderm in order to give rise to a entirely new organ. They also give an indication that the ancestral role of the FoxE gene family was probably limited to the differentiation of part of the pharynx. BioEssays 24:696–699, 2002. © 2002 Wiley Periodicals, Inc. (shrink)

Logical implications are closely related to modal operators. Lattice-valued logic LL and quantum logic QL were formulated in Titani S (1999) Lattice Valued Set Theory. Arch Math Logic 38:395–421, Titani S (2009) A Completeness Theorem of Quantum Set Theory. In: Engesser K, Gabbay DM, Lehmann D (eds) Handbook of Quantum Logic and Quantum Structures: Quantum Logic. Elsevier Science Ltd., pp. 661–702, by introducing the basic implication → which represents the lattice order. In this paper, we fomulate a predicate orthologic provided (...) with the basic implication, which corresponds to complete ortholattices, and then formulate a quantum logic which is equivalent to QL, by using a modal operator instead of the basic implication. (shrink)

Heterotrimeric G proteins, consisting of α, β, and γ subunits, couple ligand-bound seven transmembrane domain receptors to the regulation of effector proteins and production of intracellular second messengers. G protein signaling mediates the perception of environmental cues in all higher eukaryotic organisms, including yeast, Dictyostelium, plants, and animals. The nematode Caenorhabditis elegans is the first animal to have complete descriptions of its cellular anatomy, cell lineage, neuronal wiring diagram, and genomic sequence. In a recent paper, Jansen et al.(1) used sequence (...) searches of the C. elegans genome database to identify all heterotrimeric G protein genes (20 Gα, 2 Gβ, 2 Gγ). C. elegans encodes one ortholog of each of the four Gα classes found in metazoans and 16 new Gα genes. The orthologous genes are widely expressed, whereas 14 of the divergent Gα genes are almost exclusively expressed in sensory neurons where they may regulate perception and chemotaxis.BioEssays 21:713–717, 1999. © 1999 John Wiley & Sons, Inc. (shrink)

Prokaryotic genomes of endosymbionts and parasites are examples of naturally evolved minimal cells, the study of which can shed light on life in its minimum form. Their diverse biology, their lack of a large set of orthologous genes and the existence of essential linage (and environmentally) specific genes all illustrate the diversity of genes building up naturally evolved minimal cells. This conclusion is reinforced by the fact that sometimes the same essential function is performed by genes from different evolutionary origins. (...) Nevertheless, all cells perform a set of life‐essential functions however different their cell machinery and environment in which they thrive. An upcoming challenge for biologists will be to discern, by studying differences and similarities in current biodiversity, how cells with reduced genomes have adapted while retaining all basic life‐supporting functions. (shrink)

While it is generally agreed that the concept of homology refers to individuated traits that have been inherited from common ancestry, we still lack an adequate account of trait individuation or inheritance. Here I propose that we utilize a counterfactual criterion of causation to link each trait with a developmental-causal (DC) gene. A DC gene is made up of the genetic information (which might or might not be physically contiguous in the genome) that is needed for the production of the (...) organismic attributes that comprise the trait. I argue that individuated traits—phenes—correspond to organismic features that are caused by DC genes. Using such an approach, we can define a DC map, which shows the relations between each pair of phenes and provides a succinct summary of genotype-phenotype relationships and phenotypic complexity. Phenes in parents and offspring are judged to be homologous if their DC genes are composed of orthologous genetic factors. When comparing more distantly related organisms, traits are homologous when linked by a chain of parent-offspring homologs along the path of ancestry that links the two organisms. There are three possible ways to deal with the potential for multiple equivalent DC genes: maximal, minimal, and consensus homology. Whereas maximal homology has limited utility, the other two approaches have value and can help to guide research at the intersection of evolution and development. (shrink)

Like most bilaterian animals, the annelid Platynereis dumerilii generates the majority of its body axis in an anterior to posterior temporal progression with new segments added sequentially. This process relies on a posterior subterminal proliferative body region, known as the "segment addition zone" (SAZ). We explored some of the molecular and cellular aspects of posterior elongation in Platynereis, in particular to test the hypothesis that the SAZ contains a specific set of stem cells dedicated to posterior elongation.We cloned and characterized (...) the developmental expression patterns of orthologs of 17 genes known to be involved in the formation, behavior, or maintenance of stem cells in other metazoan models. These genes encode RNA-binding proteins(e.g., tudor, musashi, pumilio) or transcription factors(e.g., myc, id, runx) widely conserved in eumetazoans. Most of these genes are expressed both in the migrating primordial germ cells and in overlapping ring-like patterns in the SAZ, similar to some previously analyzed genes(piwi, vasa). The SAZ patterns are coincident with the expression of proliferation markers cyclin B and PCNA. EdU pulse and chase experiments suggest that new segments are produced through many rounds of divisions from small populations of teloblast-like posterior stem cells. The shared molecular signature between primordial germ cells and posterior stem cells in Platynereis thus corresponds to an ancestral "stemness" program. (shrink)

Ancient pathways promoting unicellularity and multicellularity are associated with cancer, the former being pro‐oncogenic and the latter acting to suppress oncogenesis. However, there are only a limited number of non‐vertebrate models for studying these pathways. Here, we review Dictyostelium discoideum and describe how it can be used to understand these gene networks. D. discoideum has a unicellular and multicellular life cycle, making it possible to study orthologs of cancer‐associated genes in both phases. During development, differentiated amoebae form a fruiting (...) body composed of a mass of spores that are supported atop a stalk. A portion of the cells sacrifice themselves to become non‐reproductive stalk cells. Cheating disrupts the principles of multicellularity, as cheater cells alter their cell fate to preferentially become spores. Importantly, D. discoideum has gene networks and several strategies for maintaining multicellularity. Therefore, D. discoideum can help us better understand how conserved genes and pathways involved in multicellularity also influence cancer development, potentially identifying new therapeutic avenues. (shrink)

To localize wheat ESTs on chromosomes, 882 homoeologous group 6-specific ESTs were identified by physically mapping 7965 singletons from 37 cDNA libraries on 146 chromosome, arm, and sub-arm aneuploid and deletion stocks. The 882 ESTs were physically mapped to 25 regions flanked by 23 deletion breakpoints. Of the 5154 restriction fragments detected by 882 ESTs, 2043 were localized to group 6 chromosomes and 806 were mapped on other chromosome groups. The number of loci mapped was greatest on chromosome 6B and (...) least on 6D. The 264 ESTs that detected orthologous loci on all three homoeologs using one restriction enzyme were used to construct a consensus physical map. The physical distribution of ESTs was uneven on chromosomes with a tendency toward higher densities in the distal halves of chromosome arms. About 43% of the wheat group 6 ESTs identified rice homologs upon comparisons of genome sequences. Fifty-eight percent of these ESTs were present on rice chromosome 2 and the remaining were on other rice chromosomes. Even within the group 6 bins, rice chromosomal blocks identified by 1-6 wheat ESTs were homologous to up to 11 rice chromosomes. These rice-block contigs were used to resolve the order of wheat ESTs within each bin. (shrink)

One of the unique insights provided by the growing number of fully sequenced genomes is the pervasiveness of gene duplication and gene loss. Indeed, several metrics now suggest that rates of gene birth and death per gene are only 10–40% lower than nucleotide substitutions per site, and that per nucleotide, the consequent lineage‐specific expansion and contraction of gene families may play at least as large a role in adaptation as changes in orthologous sequences. While gene family evolution is pervasive, it (...) may be especially important in our own evolution since it appears that the “revolving door” of gene duplication and loss has undergone multiple accelerations in the lineage leading to humans. In this paper, we review current understanding of gene family evolution including: methods for inferring copy number change, evidence for adaptive expansion and adaptive contraction of gene families, the origins of new families and deaths of previously established ones, and finally we conclude with a perspective on challenges and promising directions for future research. (shrink)

Three decades ago Gilbert posited that novel proteins arise by re‐shuffling genomic sequences encoding polypeptide domains. Today, with numerous genomes and countless genes sequenced, it is well established that recombination of sequences encoding polypeptide domains plays a major role in protein evolution. There is, however, less evidence to suggest how the novel polypeptide domains, themselves, arise. Recent comparisons of genomes from closely related species have revealed numerous species‐specific exons, supporting models of domain origin based on “exonization” of intron sequences. Also, (...) a mechanism for the origin of novel polypeptide domains has been proposed based on analyses of insertion‐based polymorphisms between orthologous genes across broad phylogenetic spectra and between allelic variants of genes within species. This review discusses these processes and how each might participate in the evolutionary emergence of novel polypeptide domains. BioEssays 29: 262–270, 2007. © 2007 Wiley Periodicals, Inc. (shrink)

Comparative genomics has proven a fruitful approach to acquire many functional and evolutionary insights into core cellular processes. Here it is argued that in order to perform accurate and interesting comparative genomics, one first and foremost has to be able to recognize, postulate, and revise different evolutionary scenarios. After all, these studies lack a simple protocol, due to different proteins having different evolutionary dynamics and demanding different approaches. The authors here discuss this challenge from a practical (what are the observations?) (...) and conceptual (how do these indicate a specific evolutionary scenario?) viewpoint, with the aim to guide investigators who want to analyze the evolution of their protein(s) of interest. By sharing how the authors draft, test, and update such a scenario and how it directs their investigations, the authors hope to illuminate how to execute molecular evolution studies and how to interpret them. Also see the video abstract here https://youtu.be/VCt3l2pbdbQ. (shrink)

Studies on the conservation of the inferred transcriptional regulatory network of prokaryotes have suggested that specific transcription factors are less‐widely conserved in comparison to their target genes. This observation implied that, at large evolutionary distances, the turnover of specific transcription factors through loss and non‐orthologous displacement might be a major factor in the adaptive radiation of prokaryotes. However, the recent work of Hershberg and Margalit1 suggests that, at shorter phylogenetic scales, the evolutionary dynamics of the bacterial transcriptional regulatory network might (...) exhibit distinct patterns. The authors find previously unnoticed relationships between the regulatory mode (activation or repression), the number of regulatory interactions and their conservation patterns in γ‐proteobacteria. These relationships might be shaped by the differences in the adaptive value and mode of operation of different regulatory interactions. BioEssays 29:625–629, 2007. © 2007 Wiley Periodicals, Inc. (shrink)

In contrast to the biallelic expression of most genes, expression of genes subject to genomic imprinting is monoallelic and based on the sex of the transmitting parent. Possession of only a single active allele can lead to deleterious health consequences in humans. Aberrant expression of imprinted genes, through either genetic or epigenetic alterations, can result in developmental failures, neurodevelopmental and neurobehavioral disorders and cancer. The evolutionary emergence of imprinting occurred in a common ancestor to viviparous mammals after divergence from the (...) egg‐laying monotremes. Current evidence indicates that imprinting regulation in metatherian mammals differs from that in eutherian mammals. This suggests that imprinting mechanisms are evolving from those that were established 150 million years ago. Therefore, comparing genomic sequence of imprinted domains from marsupials and eutherians with those of orthologous regions in monotremes offers a potentially powerful bioinformatics approach for identifying novel imprinted genes and their regulatory elements. Such comparative studies will also further our understanding of the molecular evolution and phylogenetic distribution of imprinted genes. BioEssays 25:577–588, 2003. © 2003 Wiley Periodicals, Inc. (shrink)

A common belief is that evolution generally proceeds towards greater complexity at both the organismal and the genomic level, numerous examples of reductive evolution of parasites and symbionts notwithstanding. However, recent evolutionary reconstructions challenge this notion. Two notable examples are the reconstruction of the complex archaeal ancestor and the intron‐rich ancestor of eukaryotes. In both cases, evolution in most of the lineages was apparently dominated by extensive loss of genes and introns, respectively. These and many other cases of reductive evolution (...) are consistent with a general model composed of two distinct evolutionary phases: the short, explosive, innovation phase that leads to an abrupt increase in genome complexity, followed by a much longer reductive phase, which encompasses either a neutral ratchet of genetic material loss or adaptive genome streamlining. Quantitatively, the evolution of genomes appears to be dominated by reduction and simplification, punctuated by episodes of complexification. (shrink)

Tolerance spaces are sets equipped with a reflexive, symmetric, but not necessarily transitive, relation of indistinguishability, and are useful for describing vagueness based on error-prone measurements. We show that any tolerance space can be embedded in one generated by comparisons using prototypical objects. As a result propositions, definable on a tolerance space can be translated into propositions behaving classically.

Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal logics via algebraic representation theorems. We begin with complete lattices L equipped with an antitone operation ¬ sending 1 to 0, a completely multiplicative operation ◻, and a completely additive operation ◊. Such lattice expansions can be represented by means of a set X together with binary relations (...) ⊲, R, and Q, satisfying some first-order conditions, used to represent (L,¬), ◻, and ◊, respectively. Indeed, any lattice L equipped with such a ¬, a multiplicative ◻, and an additive ◊ embeds into the lattice of propositions of a frame (X,⊲,R,Q). Building on our recent study of "fundamental logic", we focus on the case where ¬ is dually self-adjoint (a≤¬b implies b≤¬a) and ◊¬a≤¬◻a. In this case, the representations can be constrained so that R=Q, i.e., we need only add a single relation to (X,⊲) to represent both ◻ and ◊. Using these results, we prove that a system of fundamental modal logic is sound and complete with respect to an elementary class of bi-relational structures (X,⊲,R). (shrink)