How can you patent genes?

What accounts for the continued lack of clarity over the legal procedures for the patenting of DNA sequences? The patenting system was built for a "bricks-and-mortar" world rather than an information economy. The fact that genes are both material molecules and informational systems helps explain the difficulty that the patent system is going to continue to have.     

Patenting and the Gender Gap: Should Women Be Encouraged to Patent More?

The commercialization of academic science has come to be understood as economically desirable for institutions, individual researchers, and the public. Not surprisingly, commercial activity, particularly that which results from patenting, appears to be producing changes in the standards used to evaluate scientists’ performance and contributions. In this context, concerns about a gender gap in patenting activity have arisen and some have argued for the need to encourage women to seek more patents. They believe that because academic advancement is mainly dependent on productivity (Stuart and Ding in American Journal of Sociology 112:97–144, 2006; Azoulay et al. in Journal of Economic Behavior & Organization 63:599–623, 2007), differences in research output have the power to negatively impact women’s careers. Moreover, in the case of patenting activity, they claim that the gender gap also has the potential to negatively affect society. This is so because scientific and technological advancement and innovation play a crucial role in contemporary societies. Thus, women’s more limited involvement in the commercialization of science and technology can also be detrimental to innovation itself. Nevertheless, calls to encourage women to patent on grounds that such activity is likely to play a significant role in the betterment of both women’s careers and society seem to be based on two problematic assumptions: (1) that the methods to determine women’s productivity in patenting activities are an appropriate way to measure their research efforts and the impact of their work, and (2) that patenting, particularly in academia, benefits society. The purpose of this paper is to call into question these two assumptions.     

A Cut-Free Sequent System for the Smallest Interpretability Logic

The idea of interpretability logics arose in Visser [Vis90]. He introduced the logics as extensions of the provability logic GLwith a binary modality . The arithmetic realization of A B in a theory T will be that T plus the realization of B is interpretable in T plus the realization of A (T + A interprets T + B). More precisely, there exists a function f (the relative interpretation) on the formulas of the language of T such that T + B C implies T + A f(C).The interpretability logics were considered in several papers. An arithmetic completeness of the interpretability logic ILM, obtained by adding Montagna's axiom to the smallest interpretability logic IL, was proved in Berarducci [Ber90] and Shavrukov [Sha88] (see also Hájek and Montagna [HM90] and Hájek and Montagna [HM92]). [Vis90] proved that the interpretability logic ILP, an extension of IL, is also complete for another arithmetic interpretation. The completeness with respect to Kripke semantics due to Veltman was, for IL, ILMand ILP, proved in de Jongh and Veltman [JV90]. The fixed point theorem of GLcan be extended to ILand hence ILMand ILP(cf. de Jongh and Visser [JV91]). The unary pendant "T interprets T + A" is much less expressive and was studied in de Rijke [Rij92]. For an overview of interpretability logic, see Visser [Vis97], and Japaridze and de Jongh [JJ98].In this paper, we give a cut-free sequent system for IL. To begin with, we give a cut-free system for the sublogic IL4of IL, whose -free fragment is the modal logic K4. A cut-elimination theorem for ILis proved using the system for IK4and a property of Löb's axiom.     

Paraconsistent algebras

The prepositional calculiC _n , 1 n introduced by N.C.A. da Costa constitute special kinds of paraconsistent logics. A question which remained open for some time concerned whether it was possible to obtain a Lindenbaum's algebra forC _n . C. Mortensen settled the problem, proving that no equivalence relation forC _n . determines a non-trivial quotient algebra.The concept of da Costa algebra, which reflects most of the logical properties ofC _n , as well as the concept of paraconsistent closure system, are introduced in this paper.We show that every da Costa algebra is isomorphic with a paraconsistent algebra of sets, and that the closure system of all filters of a da Costa algebra is paraconsistent.     

Graded modalities. I

We study a modal system ¯T, that extends the classical (prepositional) modal system T and whose language is provided with modal operators M inn (nN) to be interpreted, in the usual kripkean semantics, as there are more than n accessible worlds such that.... We find reasonable axioms for ¯T and we prove for it completeness, compactness and decidability theorems.The authors are very indebted to the referee for Ms consideration and appreciation of their work.     

The completeness of S

The subsystem S of Parry's AI [10] (obtained by omitting modus ponens for the material conditional) is axiomatized and shown to be strongly complete for a class of three valued Kripke style models. It is proved that S is weakly complete for the class of consistent models, and therefore that Ackermann's rule is admissible in S. It also happens that S is decidable and contains the Lewis system S4 on translation — though these results are not presented here. S is arguably the most relevant relevant logic known at this time to be decidable.I wish to thank Jill Pipher and Professora Nuel D. Belnap, Jr. and David Kaplan for their helpful comments on an earlier version of this paper.     

Undecidability and intuitionistic incompleteness

Let S be a deductive system such that S-derivability (s) is arithmetic and sound with respect to structures of class K. From simple conditions on K and s, it follows constructively that the K-completeness of s implies MP(S), a form of Markov's Principle. If s is undecidable then MP(S) is independent of first-order Heyting arithmetic. Also, if s is undecidable and the S proof relation is decidable, then MP(S) is independent of second-order Heyting arithmetic, HAS. Lastly, when s is many-one complete, MP(S) implies the usual Markov's Principle MP.An immediate corollary is that the Tarski, Beth and Kripke weak completeness theorems for the negative fragment of intuitionistic predicate logic are unobtainable in HAS. Second, each of these: weak completeness for classical predicate logic, weak completeness for the negative fragment of intuitionistic predicate logic and strong completeness for sentential logic implics MP. Beth and Kripke completeness for intuitionistic predicate or sentential logic also entail MP.These results give extensions of the theorem of Gödel and Kreisel (in [4]) that completeness for pure intuitionistic predicate logic requires MP. The assumptions of Gödel and Kreisel's original proof included the Axiom of Dependent Choice and Herbrand's Theorem, no use of which is explicit in the present article.     

Many-Valued Points And Equality

In 1999, da Silva, D'Ottaviano and Sette proposed a general definition for the term translation between logics and presented an initial segment of its theory. Logics are characterized, in the most general sense, as sets with consequence relations and translations between logics as consequence-relation preserving maps. In a previous paper the authors introduced the concept of conservative translation between logics and studied some general properties of the co-complete category constituted by logics and conservative translations between them. In this paper we present some conservative translations involving classical logic, Lukasiewicz three-valued system L ₃, the intuitionistic system I ¹ and several paraconsistent logics, as for instance Sette's system P ¹, the D'Ottaviano and da Costa system J ₃ and da Costa's systems C _n, 1 n.     

Cut-free sequent and tableau systems for propositional Diodorean modal logics

We present sound, (weakly) complete and cut-free tableau systems for the propositional normal modal logicsS4.3, S4.3.1 andS4.14. When the modality is given a temporal interpretation, these logics respectively model time as a linear dense sequence of points; as a linear discrete sequence of points; and as a branching tree where each branch is a linear discrete sequence of points.Although cut-free, the last two systems do not possess the subformula property. But for any given finite set of formulaeX the superformulae involved are always bounded by a finite set of formulaeX* _L depending only onX and the logicL. Thus each system gives a nondeterministic decision procedure for the logic in question. The completeness proofs yield deterministic decision procedures for each logic because each proof is constructive.Each tableau system has a cut-free sequent analogue proving that Gentzen's cut-elimination theorem holds for these latter systems. The techniques are due to Hintikka and Rautenberg.Presented byDov M. Gabbay     

Rosser orderings and free variables

It is shown that for arithmetical interpretations that may include free variables it is not the Guaspari-Solovay system R that is arithmetically complete, but their system R ^–. This result is then applied to obtain the nonvalidity of some rules under arithmetical interpretations including free variables, and to show that some principles concerning Rosser orderings with free variables cannot be decided, even if one restricts oneself to usual proof predicates.     

A consistent theory of attributes in a logic without contraction

This essay demonstrates proof-theoretically the consistency of a type-free theoryC with an unrestricted principle of comprehension and based on a predicate logic in which contraction (A (A B)) (A B), although it cannot holds in general, is provable for a wide range ofA's.C is presented as an axiomatic theoryCH (with a natural-deduction equivalentCS) as a finitary system, without formulas of infinite length. ThenCH is proved simply consistent by passing to a Gentzen-style natural-deduction systemCG that allows countably infinite conjunctions and in which all theorems ofCH are provable.CG is seen to be a consistent by a normalization argument. It also shown that in a senseC is highly non-extensional.     

CE is Not a Conservative Extension of E

The logic CE (for Classical E) results from adding Boolean negation to Anderson and Belnap"s logic E. This paper shows that CE is not a conservative extension of E.     

Sex,germs, and health: pathogen-avoidance motives and health-protective behaviour

Objective: Recent work suggests that the psychology of pathogen-avoidance has wide-reaching effects on how people interact with the world. These processes – part of what has been referred to as the behavioural immune system – are, in a way, our ‘evolved’ health psychology. However, scholars have scarcely investigated how the behavioural immune system relates to health-protective behaviours. The current research attempts to fill this gap.

Design: Across two cross-sectional studies (N = 386 and 470, respectively), we examined the relationship between pathogen-avoidance motives and health-protective behaviour.

Outcome Measures: The studies used self-reported measures of attitude and intention as indicators of health-protective behaviour.

Results: Data collected in Study 1 revealed that pathogen-avoidance motivation related to participants’ attitude and intention towards sexually transmitted infections screening. High levels of pathogen-avoidance motivation were also related to having had fewer sexual partners, which partially mediated the effect of pathogen-avoidance variables on testing motivation. Study 2 extended these findings by showing moderate associations between pathogen-avoidance motivation and a broad range of health-protective behaviours, including but not limited to pathogen-related health concerns.

Conclusion: We argue that understanding and targeting pathogen-avoidance psychology can add novel and important understanding of health-protective behaviour.     

The patenting process,innovation, and size

This paper focuses on the U.S. patenting process and how large and small entity inventors respond to it. In particular, a framework of patenting process events and activities related to success is developed and evaluated empirically, with a factor analysis revealing similarities and differences in the priorities of the two groups. The results have implications for both the conduct of the new product process under the law and for review and examination of public policy regarding patents. He received his Ph.D. from Lehigh University. His research interests include intellectual capital, intellectual property, and competitive intelligence. He has published in Journal of Marketing Management, European Journal of Marketing, Journal of Marketing & Public Policy, and Industrial Marketing Management.     

Are Our Concepts conscious state and conscious creature Vague?

Intuitively it has seemed to many that our concepts conscious state and conscious creature are sharp rather than vague, that they can have no borderline cases. On the other hand, many who take conscious states to be identical to, or realized by, complex physical states are committed to the vagueness of those concepts. In the paper I argue that conscious state and conscious creature are sharp by presenting four necessary conditions for conceiving borderline cases in general, and showing that some of those conditions cannot be met with conscious state. I conclude that conscious state is sharp, and the conclusion is then extended to conscious creature. The paper ends with a brief discussion of some implications.

Virtual Modality

Model-theoretic 1-types overa given first-order theory T may be construed as natural metalogical miniatures of G. W. Leibniz' ``complete individual notions', ``substances' or ``substantial forms'. This analogy prompts this essay's modal semantics for an essentiallyundecidable first-order theory T, in which one quantifies over such ``substances' in a boolean universe V(C), where C is the completion of the Lindenbaum-algebra of T.More precisely, one can define recursively a set-theoretic translate of formulae _N of formulae of a normal modal theory T_m based on T, such that the counterpart `<sub>i</sub>' of a the modal variable `x_i' of L(T_m) in this translation-scheme ranges over elements of V(C) that are 1-types of T with value 1 (sometimes called `definite' C-valued 1-types of T).The article's basic completeness-result (2.13) then establishes that varphi; is a theorem of T<sub>m</sub> iff [[ <sub>N</sub> () is aconsequenceof <sub>N</sub> (T<sub>m</sub>) for each extension N of T which is a subtheory of the canonical generic theory (ultrafilter) u]] = 1 – or equivalently, that T<sub>m</sub> is consistent iff[[there is anextension N of T such that N is a subtheory of the canonical generic theory u, and <sub>N</sub>() for all in T<sub>m</sub>]] > 0.The proof of thiscompleteness-result also shows that an N which provides a countermodel for a modally unprovable – or equivalently, a closed set in the Stone space St(T) in the sense of V(C) – is intertranslatable with an `accessibility'-relation of a closely related Kripke-semantics whose `worlds' are generic extensions of an initial universe V via C.This interrelation providesa fairly precise rationale for the semantics' recourse to C-valued structures, and exhibits a sense in which the boolean-valued context is sharp.     

Axiomatization and completeness of uncountably valued approximation logic

A first order uncountably valued logicL _Q(0,1) for management of uncertainty is considered. It is obtained from approximation logicsL _T of any poset type (T, ) (see Rasiowa [17], [18], [19]) by assuming (T, )=(Q(0, 1), ) — whereQ(0, 1) is the set of all rational numbersq such that 0<q<1 and is the arithmetic ordering — by eliminating modal connectives and adopting a semantics based onLT-fuzzy sets (see Rasiowa and Cat Ho [20], [21]). LogicL _Q(0,1) can be treated as an important case ofLT-fuzzy logics (introduced in Rasiowa and Cat Ho [21]) for (T, )=(Q(0, 1), ), i.e. asLQ(0, 1)-fuzzy logic announced in [21] but first examined in this paper.L _Q(0,1) deals with vague concepts represented by predicate formulas and applies approximate truth-values being certain subsets ofQ(0, 1). The set of all approximate truth-values consists of the empty set ø and all non-empty subsetss ofQ(0, 1) such that ifqs andqq, thenqs. The setLQ(0, 1) of all approximate truth-values is uncountable and covers up to monomorphism the closed interval [0, 1] of the real line.LQ(0, 1) is a complete set lattice and therefore a pseudo-Boolean (Heyting) algebra. Equipped with some additional operations it is a basic plain semi-Post algebra of typeQ(0, 1) (see Rasiowa and Cat Ho [20]) and is taken as a truth-table forL _Q(0,1) logic.L _Q(0,1) can be considered as a modification of Zadeh's fuzzy logic (see Bellman and Zadeh [2] and Zadeh and Kacprzyk, eds. [29]). The aim of this paper is an axiomatization of logicL _Q(0,1) and proofs of the completeness theorem and of the theorem on the existence ofLQ(0, 1)-models (i.e. models under the semantics introduced) for consistent theories based on any denumerable set of specific axioms. Proofs apply the theory of plain semi-Post algebras investigated in Cat Ho and Rasiowa [4].Presented byCecylia Rauszer     

Models for stronger normal intuitionistic modal logics

This paper, a sequel to Models for normal intuitionistic modal logics by M. Boi and the author, which dealt with intuitionistic analogues of the modal system K, deals similarly with intuitionistic analogues of systems stronger than K, and, in particular, analogues of S4 and S5. For these prepositional logics Kripke-style models with two accessibility relations, one intuitionistic and the other modal, are given, and soundness and completeness are proved with respect to these models. It is shown how the holding of formulae characteristic for particular logics is equivalent to conditions for the relations of the models. Modalities in these logics are also investigated.This paper presents results of an investigation of intuitionistic modal logic conducted in collaboration with Dr Milan Boi.     

Intermediate logics with the same disjunctionless fragment as intuitionistic logic

Given an intermediate prepositional logic L, denote by L ^–d its disjuctionless fragment. We introduce an infinite sequence {J _n}_n1 of propositional formulas, and prove:(1)For any L: L ^–d =I ^–d (I=intuitionistic logic) if and only if J _n L for every n 1.Since it turns out that L{J _{n} n}1 = Ø for any L having the disjunction property, we obtain as a corollary that L ^–d = I ^–d for every L with d.p. (cf. open problem 7.19 of [5]). Algebraic semantic is used in the proof of the if part of (1). In the last section of the paper we provide a characterization in Kripke's semantic for the logics J _n =I+ +J _n (n 1).     

Open questions related to the problem of Birkhoff and Maltsev

The Birkhoff-Maltsev problem asks for a characterization of those lattices each of which is isomorphic to the lattice L(K) of all subquasivarieties for some quasivariety K of algebraic systems. The current status of this problem, which is still open, is discussed. Various unsolved questions that are related to the Birkhoff-Maltsev problem are also considered, including ones that stem from the theory of propositional logics.Special issue of Studia Logica: Algebraic Theory of Quasivarieties Presented by Ryszard Wójcicki