Jean-Yves Girard. The blind spot – lectures on logic. European Mathematical Society, 2011.  Giuseppe Longo, Kathleen Milsted, and Sergei Soloviev. Coherence and transitivity of subtyping
as entailment. Journal of Logic and Computation, 10(4):493–526, 2000.
 Zhaohui Luo. Contextual analysis of word meanings in type-theoretical semantics. In Sylvain Pogodalla and Jean-Philippe Prost, editors, LACL, volume 6736 of LNCS, pages 159–174. Springer, 2011.
mals” also apply to “human beings”). Coercive subtyping  sounds promising for F. Its key
property is that, if at most one subtyping map is given between any two base types, then there also is at most one subtyping map between any two complex types. Predefined (inductive) types, e.g. integers as in G¨ odel’s system T and finite sets of α-objects with their reduction schemes as in  are also welcome — encodings in F are cumbersome. The key points are normalisation, confluence and the absence of closed constant-free terms in any false type. We shall also illustrate the linguistic relevance of these extensions, which are already included in Moot’s semantical and semantical parser for French named Grail. 
Regarding coercions, Luo  makes an extensive use of coercive subtyping, which he introduced with Soloviev : as said in their paper this kind of subtyping may also work well with system F. So we can say that the system of Luo is very similar. Dependent types and predicative quantification may be closer to what we wish to model, but the formal diversity of the numerous employed rules may result in an obscure formalisation. The typed system at work in Asher’s view  is a simple type theory extended with type constructors and operations imported from category theory. The theory extends cartesian closed category with a few of the many operations that one finds in topos theory, like being a subobject. This approach is difficult to compare with the two above, since it does not belong to the same family: morphisms do not represent (quotiented) proofs of some logic, they are closer to a set theoretic interpretation.
(18) a. The students wrote a paper. (unambiguous) b. The students wrote three papers. (covering)
Such readings are derivable in our model because one can define in F operators for handling plurals. Firstly, one can add, as a constant, a cardinality operator for predicates ||_|| : Πα. (α → t) → N where N are the internal integers of system F, namely N = ΠX. (X → X) → (X → X), or a predefined integer type as in Gödel system T – this might be problematic if infinitely many objects satisfied the predicate, but syntax and restriction of selection can make sure it is only applied when it makes sense. Secondly, as shown in Figure 5, we can have operators for handling plurals: q (turning an individual into a property/set, a curried version of equality), ∗ (distributivity), # (restricted distributivity from sets of sets to its constituent subsets), c (for coverings), etc. The important fact is that the computation of such readings uses exactly the same mechanisms as lexical coercion. Some combinations are blocked by their types, but optional terms coming either from the predicate or from the plural noun may allow an a priori prohibited reading. To be precise we also provide specific tools for handling groups that are singular nouns, each of which denoting a set. All these functions are easily implemented in a typed functional programming language like Haskell, in the style of .
Usually, F N depends only on name(N). In this case, we also write the function F name(N ) . Consider for
instance indefinites, which are interpreted with the quantifier a. In most cases, F a = λ(P, Q) .λx.P x∧Q x,
but in some cases, such as donkey sentences, the function depends on the context of the vertex N. The interest of using semantic graphs is to facilitate the computation of F N . Most times, F name(N ) reduces to a
X. R ELATED W ORKS
The phenomenon of self-adjunction is mentioned by Kock  and stressed by Thielecke  in his work on continuations. The notion of dialogue category was inspired by the key observation by Hofmann and Streicher  and then Selinger  that every denotational model of classical logic (that is, of the λµ-calculus) boils down to a continuation model. The formulation of dialogue categories as dialogue chiralities was inspired by Girard’s work on polarities in LC  and its relationship to dialogue games noticed by Laurent , together with the correspondence between games, polarities and continuations originally investigated with Selinger . Note that similar ideas of symmetry appeared independently in the work by Cockett and Seely . The game-theoretic description of the maps f : X → Y between atoms in X as labelled pointers between atomic moves is reminiscent of the game-theoretic account of Girard’s geometry of interaction  and ofproof-nets ,  together with the graphical description of the free ribbon category  discussed in the introduction. On the proof-theoretic side, this work should be compared with similar graphical descriptions of the free ∗-autonomous category  and of the free symmetric monoidal closed category . One main difference with the present work is that both constructions ,  require to identify diagrams modulo Trimble’s rewiring equalities  and thus to depart from the purely topological and diagrammatic notion ofproof equality underlying dialogue categories.
The linear nature of resource calculus enables it to be considered as a suitable target lan- guage for the linearisation of ordinary λ-calculus. The graphical syntax of resource inter- action nets enhances such linearisation with a tight correspondence at the level of Linear Logic types: boxes’ content is duplicated with any arbitrary cardinality (thus also erased), promotions becomes co-contractions, boxes themselves are forgotten, and linear implica- tions just preserved. A quick look at Figure 4.1 provides the visual intuition. Each boxing- depth-recursive choice of those cardinalities is a simple resource net, while the (possibly infinite) series of all of them is a resource net, called the Taylor-Ehrhard-Regnier expan- sion of the original proof-net. Probably inspired by Girard ’s notion of approximants of the exponential modality [ 1987 ], the expansion was originally formulated by Ehrhard and Regnier [ 2008 ] as a map from λ-terms to differential λ-terms, and then simplified to be targeted into its linear fragment, the resource calculus, expansion was also refined in a typed net-like counterpart, employing not only the call-by-name translation that we con- sider here [ Mazza and Pagani , 2007 , Pagani and Tasson , 2009 ], but also the call-by-value discipline [ Carraro and Guerrieri , 2014 ]. Given that resource nets strongly normalise, the expansion of a term can be interpreted as the series of its finite approximations, hence the link with Taylor series and the notion of differentiation.
Moreover, the fact (not much developed in this extended abstract) that a design may be viewed either as a kind ofproof (in a syntactic setting of the framework) or as a game (in a semantic setting of it) provides us with interesting insights on Pragmatics and Wittgensteinian language games. In a pragmatic theory of presupposition, for instance, presupposing implies making an assertion where the hearer has no access to a previous step made by the speaker, if (s)he rejects this step, (s)he makes the process to diverge. Other ”games” may be explored. Wittgenstein for instance quoted elicitation, that is the way in which some- body may obtain an answer to a question. Every time, Fax is used to transfer a meaning from a location
Besides sites, four combinators are provided by core calculus. The parallel composition expresses pure concurrency. In f |g, f and g are run in parallel, their events are interleaved and the expression stops when both f and g have terminated. As suggested by its name, the sequential operator expresses sequentiality. In the expression f > x > g, the variable x can be used in g. Here, f is started first, and then a new instance of g[v/x], where x is bounded to v, is launched as a consequence of each publication of v. The third operator, called pruning, expresses preemption. In f <x< g, the variable x can be used in f . Both f and g are started at once, but f is paused when it needs to evaluate x. When g publishes a value, it is bounded to x in f and g is stopped. The other events that could have been produced by g are preempted by the publication. For example, if g is supposed to publish two values a and b, only one will be selected and published in each execution. We say that these two events are in conflict. The last operator is called otherwise. In f ; g, f is first started alone and g is started if and only if f stops without publishing any value.
This being said, fuzzy logics have been widely criticised ((Kamp, 1975; Williamson, 1994; Edgington, 1997) among many others). Most objections to fuzzy approaches derive from one feature of fuzzy systems that is hard to swallow, namely that flat contradictions receive values in the range [0, 0.5]. Many have reacted negatively to the idea that a flat contradiction can be anything other than completely false. Yet, things are worse for fuzzy logic than that. As we saw in section 3.1, there have been empirical observations that “F and not F ” responses to borderline cases of vague predicates are common. Perhaps, then, flat contradictions needn’t always be false as the philosophical orthodoxy would suggest. However, taking these diverging intuitions at face value, either a flat contradiction should be valued as totally false, or, in borderline cases, as totally acceptable/true. Unfortunately for fuzzy logic, flat contradictions made about central borderline cases receive values of 0.5 which satisfies neither intuition. That said, one could defend a view that intuitions regarding flat contradictions track acceptability as opposed to limit-value degrees of truth. If this were so, then, provided that, for example, the acceptability of an outright assertion of a flat contradiction could be, say 0 when its degree of truth value is 0.5, then some intuitions can be accommodated. (See e.g. Smith (2008) for such a proposal.) Ultimately, the success of such a position will turn on defending the view that intuitions surrounding contradictions track acceptability and not (absolute) falsity. Other challenges arise, too. For example, a sorites argument could now be formulated surrounding acceptability, namely a metasemantic HOV problem (see Wright (1975) for discussion, Smith (2008) for a reply, and Sutton (2017) for discussion of difficulties with proposals such as Smith’s).
The Chen group at the National Institute of Biomedical Imaging and Bioengineering of the National Institutes of Health uses nanomaterials as platforms to provide imaging contrast in positron emission tomography (PET). In medical imaging, PET can provide a direct, highly sensitive, and quantitative readout of organ/tissue targeting efficiency and pharmacokinetics. Compared with radiolabeled antibodies, proteins, peptides, and other biologically relevant molecules, radiolabeled nanoparticles represent a new frontier in molecular imaging probe design because they can combine different imaging modalities and targeting ligands in a single vector, synergistically improving the imaging quality. 56 However, the applications of radiolabeled nanoparticles are based on the premise that the radioisotopes are stably attached to the nanomaterials. Chen has developed general rules for selecting appropriate isotopes for given types of nanoparticles as well as adjusting the labeling reaction according to specific applications. The stability (colloidal and radiochemical) of the radiolabeled nanoparticles as well as their biological fate must be assessed; special attention should be paid to labeling strategies as they affect the stability of radiolabeled nanoparticles and might cause discrepancies in the interpretation of PET data (owing to the distribution of nanoparticles). Wang’s group at the Chinese Academy of Sciences is interested in creating nano–bio interfaces with controllable adhesion properties. The cell-adhesive biointerfaces are based on the cooperative effects of multiscale structural matching and molecular recognition. 57 They explore the relationship between cell-specific adhesion and surface structure (with
Lost in post-translation
Olivier Putois 1 , François Villa 1 & Jonathan B Weitzman 2
S hakespeare suggested that names are of little importance and that “A rose, by any other name would smell as sweet” , but we beg to differ. The names that we choose to describe processes and concepts— biological or otherwise—profoundly influence the way we think about them. This is brought home when interdisciplinary research gathers together colleagues from diverse fields who struggle to understand what familiar words mean in new intellectual contexts. As biologi- cal research becomes increasingly interdisci- plinary, the use of “shared but different” technical terms becomes increasingly fraught. For example, biologists share many terms with computer scientists that describe both biological and digital phenomena, and communication becomes even more demand- ing when interacting with colleagues from the social sciences, for whom words can have completely different meanings. The difficul- ties are heightened with those terms that bio- logists have outright appropriated from other disciplines—albeit with good reason—but in doing so have stripped away their original nuance and meaning.
Our final goal is to have both an abstract language dissociated from the concrete languages and an extensible abstract machine to process them. In particular this al- lows us to define parameterizable graph operators for instance to revisit classical structural metrics and adapt their definition to go beyond the pure structural calcula- tion and take into account the types in the graphs. In the longer term, we intend to perform search (e.g. homomorphism) and logical derivation (e.g. homomorphism and merge) but also approximation (e.g. distances), clustering (e.g. propagation), analysis (e.g. centrality), etc. jointly on the same graphs. We target the design of an abstract graph machine  generalizing operations needed by and sometime shared across different languages (e.g. SPARQL, RIF, POWDER, RDF/S and OWL inferences) and operations. In addition we also believe it is interesting to study alternatives to OWL stack and the associated DL-reasoning. For instance a rule-based semantic web with an alternative stack (RDF/S + SPARQL + Rules) provides certain advantages: rules are often more natural for humans, they support event-based programming and web service integration, they are usable both for domain independent and domain depen- dent inferences, etc.
Keywords scope ambiguities, theta-roles, minimalist gram- mars, categorial grammars, λµ-calculus
Many works have been done on Type-Theoretical Grammars since the famous books by Glyn Morrill (Morrill (1994)) and Aarne Ranta (Ranta (1994)), respectively based on the Categorial tradition (Lam- bek (1958), Moortgat (1997)) and on Martin-L¨ of’s Constructive Type Theory. More recently, much has been done, exploiting Curry’s distinc- tion between the tectogrammatical and the phenogrammatical levels, and this has led to interesting proposals like Lambda Grammars, Ab- stract Categorial Grammars and Convergent Grammars (de Groote (2001a), Muskens (2003), Pollard (2007)). Type-theoretic formulations of Minimalist Grammars have also been proposed (Lecomte and Retor´e (2001), Amblard (2007), Lecomte (2005), Anoun and Lecomte (2006)). All these works take care of problems like scope ambiguities which are traditional in the Montagovian perspective but they pay little attention to thematic roles and binding phenomena (except Anoun and Lecomte (2006) and Pollard (2007)). These questions have been more widely
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Several structural and biochemical studies have shown that residues of the basic loop of eIF1 were important for the binding of the factor to the ribosome ( 14 , 15 , 17 , 18 , 57 ). Moreover, the cryo-EM structure of a Pa-PIC containing all initiation factors showed that aIF1 was bound to the ri- bosome in a manner equivalent to its eukaryotic homolog ( 24 ). Here, we show that R31, Y32 and K34 of the basic loop of Pa-aIF1 participate in the binding to the 30S. Moreover, some residues, such as Y32, are involved in the stabilization of the 30S:mRNA conformation (Table 1 , Supplementary Figure S6). Notably, although the basic character of loop 1 is conserved in archaea and eukaryotes, the consensus se- quences in the two phyla are idiosyncratic (Figure 1 C). An- other notable difference between eukaryotic and archaeal e /aIF2 and their homologues corresponds to the absence of the acidic loop 2 in the archaeal kingdom, as observed here and in ( 46 ). In eukaryotes, the acidic loop 2 was shown to participate in start codon selection by interacting with the D-stem-loop of the initiator tRNA ( 17 , 58 ). In addition, many archaeal aIF1 possess a zinc-binding knuckle in their N-terminal domain whereas this is never observed in eu- karyotic species. This may reflect adaptation of the role of e /aIF1 to either long-range or local scanning mechanism. Interestingly, variations of the loop 1 and loop 2 sequences were also noted in the SUI1 homologous domains of eIF2D and DENR implicated in eukaryotic re-initiation, another different mechanism for start codon selection ( 59 , 60 ).
In this chapter, we have presented a determinate checker written in OCaml side by side with a formalization of this MaxChecker in Coq which was restricted to the propositional fragment. In extending this treatment to the quantifiers, and with them to full first-order logic, the handling of bindings predictably becomes the principal point of interest. In Coq, bindings are not first-class constructs of the language and must therefore be explicitly modeled and their metatheory proved; several Coq libraries facilitate facilitate work with bindings and mitigate the increase in the complexity of proofs. Our use of Prop as the type of atoms is a further complication that needs to be addressed. A simplifying factor lifted from the OCaml checker consists of fixing a single type of terms—over which quantification may occur—mimicking the kernel in Figure 4.3 and those to come in Part III. An aspect of the OCaml code which resists easy formalization is the representation of bindings by function spaces in the encoding of higher-order abstract syntax. Adopting functions leads to so-called exotic terms and are far more general than the limited operation of substitution they are expected to represent (Despeyroux et al., 1995).