bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the maximality of logics with approximations
Authors: Iovino José 
Published: May 2006

In this paper we analyze some aspects of the question of using methods from model theory to study structures of functional analysis.By a well known result of P. Lindström, one cannot extend the expressive power of first order logic and yet preserve its most outstanding model theoretic characteristics (e.g., compactness and the Löwenheim-Skolem theorem). However, one may consider extending the scope of first order in a different sense, specifically, by expanding the class of structures that are regarded as models (e.g., including Banach algebras or other structures of functional analysis), and ask whether the resulting extensions of first order model theory preserve some of its desirable characteristics.A formal framework for the study of structures based on Banach spaces from the perspective of model theory was first introduced by C. W. Henson in [8] and [6]. Notions of syntax and semantics for these structures were defined, and it was shown that using them one obtains a model theoretic apparatus that satisfies many of the fundamental properties of first order model theory. For instance, one has compactness, Löwenheim-Skolem, and omitting types theorems. Further aspects of the theory, namely, the fundamentals of stability and forking, were first introduced in [10] and [9].The classes of mathematical structures formally encompassed by this framework are normed linear spaces, possibly expanded with additional structure,e.g., operations, real-valued relations, and constants. This notion subsumes wide classes of structures from functional analysis. However, the restriction that the universe of a structure be a normed space is not necessary. (This restriction has a historical, rather than technical origin; specifically, the development of the theory was originally motivated by questions in Banach space geometry.) Analogous techniques can be applied if the universe is a metric space. Now, when the underlying metric topology is discrete, the resulting model theory coincides with first order model theory, so this logic extends first order in the sense described above. Furthermore, without any cost in the mathematical complexity, one can also work in multi-sorted contexts, so, for instance, one sort could be an operator algebra while another is. say, a metric space.
Slim models of Zermelo set theory
Authors: Mathias A. R. D. 
Published: May 2006

AbstractWorking in Z + KP, we give a new proof that the class of hereditarily finite sets cannot be proved to be a set in Zermelo set theory, extend the method to establish other failures of replacement, and exhibit a formula Φ(λ, a) such that for any sequence ⟨Aλ ∣ λ a limit ordinal⟩ where for each λ. Aλ ⊆ λ2, there is a supertransitive inner model of Zermelo containing all ordinals in which for every λAλ = {a ∣ Φ(λ, a)}.
Applications of PCF theory
Authors: Shelah Saharon 
Published: May 2006

AbstractWe deal with several pcf problems: we characterize another version of exponentiation: maximal number ofk-branches in a tree withλnodes, deal with existence of independent sets in stable theories, possible cardinalities of ultraproducts and the depth of ultraproducts of Boolean Algebras. Also we give cardinal invariants for eachλwith a pcf restriction and investigate furtherTD{f). The sections can be read independently, although there are some minor dependencies.
Hybrid logics: characterization, interpolation and complexity
Authors: Areces Carlos , Blackburn Patrick , Marx Maarten 
Published: May 2006

AbstractHybrid languages are expansions of propositional modal languages which can refer to (or even quantify over) worlds. The use of strong hybrid languages dates back to at least [Pri67], but recent work (for example [BS98, BT98a, BT99]) has focussed on a more constrained system called H(↓, @). We show in detail that (↓, @) is modally natural. We begin by studying its expressivity, and provide model theoretic characterizations (via a restricted notion of Ehrenfeucht-Fraïssé game, and an enriched notion of bisimulation) and a syntactic characterization (in terms of bounded formulas). The key result to emerge is that (↓, @) corresponds to the fragment of first-order logic which is invariant for generated submodels. We then show that (↓, @) enjoys (strong) interpolation, provide counterexamples for its finite variable fragments, and show that weak interpolation holds for the sublanguage (@). Finally, we provide complexity results for (@) and other fragments and variants, and sharpen known undecidability results for (↓, @).
Exact bounds for lengths of reductions in typed λ-calculus
Authors: Beckmann Arnold 
Published: May 2006

AbstractWe determine the exact bounds for the length of an arbitrary reduction sequence of a term in the typed λ-calculus with β-, ξ- and η-conversion. There will be two essentially different classifications, one depending on the height and the degree of the term and the other depending on the length and the degree of the term.
Syllogism and quantification
Authors: Smiley Timothy 
Published: May 2006

Anyone who reads Aristotle, knowing something about modern logic and nothing about its history, must ask himself why the syllogistic cannot be translated as it stands into the logic of quantification. It is now more than twenty years since the invention of the requisite framework, the logic of many-sorted quantification.In the familiar first-order predicate logic generality is expressed by means of variables and quantifiers, and each interpretation of the system is based upon the choice of some class over which the variables may range, the only restriction placed on this ‘domain of individuals’ being that it should not be empty.
On the formalisation of indirect discourse
Authors: Goodstein R. L. 
Published: May 2006

Mr. L. J. Cohen's interesting example of a logical truth of indirect discourse appears to be capable of a simple formalisation and proof in a variant of first order predicate calculus. His example has the form:If A says that anything which B says is false, and B says that something which A says is true, then something which A says is false and something which B says is true.Let ‘A says x’ be formalised by ‘A(x)’ and let assertions of truth and falsehood be formalised as in the following table.We treat both variables x and predicates A (x) as sentences and add to the familiar axioms and inference rules of predicate logic a rule permitting the inference of A(p) from (x)A(x), where p is a closed sentence.We have to prove that from
The implicational fragment of Dummett's LC
Authors: Bull R. A. 
Published: May 2006

It has been shown in Dummett [1] that the system LC given by Heyting's Calculus plus the additional axiom ACpqCqp is complete with respect to the model having as truth values the integers 0, 1,2, … and ω, 0 being the designated value, with
In this system CCCpqrCCCqprr is equivalent to ACpqCqp, and the purpose of this paper is to show that the implicational fragment of Heyting's Calculus plus the additional axiom CCCpqrCCCqprr yields the implicational fragment of LC.
Degrees of unsolvability associated with classes of formalized theories
Authors: Feferman Solomon 
Published: May 2006

In his well-known paper [11], Post founded a general theory of recursively enumerable sets, which had its metamathematical source in questions about the decision problem for deducibility in formal systems. However, in centering attention on the notion of degree of unsolvability, Post set a course for his theory which has rarely returned to this source. Among exceptions to this tendency we may mention, as being closest to the problems considered here, the work of Kleene in [8] pp. 298–316, of Myhill in [10], and of Uspenskij in [15]. It is the purpose of this paper to make some further contributions towards bridging this gap.From a certain point of view, it may be argued that there is no real separation between metamathematics and the theory of recursively enumerable sets. For, if the notion of formal system is construed in a sufficiently wide sense, by taking as ‘axioms’ certain effectively found members of a set of ‘formal objects’ and as ‘proofs’ certain effectively found sequences of these objects, then the set of ‘provable statements’ of such a system may be identified, via Gödel's numbering technique, with a recursively enumerable set; and conversely, each recursively enumerable set is identified in this manner with some formal system (cf. [8] pp. 299–300 and 306). However, the pertinence of Post's theory is no longer clear when we turn to systems formalized within the more conventional framework of the first-order predicate calculus. It is just this restriction which serves to clarify the difference in spirit of the two disciplines.
New foundations for Lewis modal systems
Authors: Lemmon E. J. 
Published: May 2006

The main aims of this paper are firstly to present new and simpler postulate sets for certain well-known systems of modal logic, and secondly, in the light of these results, to suggest some new or newly formulated calculi, capable of interpretation as systems of epistemic or deontic modalities. The symbolism throughout is that of [9] (see especially Part III, Chapter I). In what follows, by a Lewis modal system is meant a system which (i) contains the full classical propositional calculus, (ii) is contained in the Lewis system S5, (iii) admits of the substitutability of tautologous equivalents, (iv) possesses as theses the four formulae:We shall also say that a system Σ1 is stricter than a system Σ2, if both are Lewis modal systems and Σ1 is contained in Σ2 but Σ2 is not contained in Σ1; and we shall call Σ1absolutely strict, if it possesses an infinity of irreducible modalities. Thus, the five systems of Lewis in [5], S1, S2, S3, S4, and S5, are all Lewis modal systems by this definition; they are in an order of decreasing strictness from S1 to S5; and S1 and S2 alone are absolutely strict.
Epimenides the Cretan
Authors: Prior A. N. 
Published: May 2006

What I am offering here is a reconsideration, and in the end a solution, of the ancient paradox of the Epimenides. What has provoked this new assault on so old a stronghold is L. Jonathan Cohen's [2], in which it is rightly pointed out that the Epimenidean as contrasted with the Eubulidean version of the Liar paradox is the one that threatens logicians who attempt to formalise the use of indirect rather than direct discourse. Among these he includes myself, referring to the system sketched on pp. 130–131 of my [4], and suggesting that I ought to have shown how a person interpreting this system in the obvious way can avoid semantic antinomies. Here too he is right, and my main purpose now is not to criticise his paper, but to fill in this lacuna in my own work to which he has drawn attention. I do want, however, to make one small criticism at the start, namely that Cohen fails to notice what it is that is really paradoxical about the Epimenides, and in consequence fails to perceive the same paradoxical character in a proposition which he is himself quite happy to accept as a ‘logical truth.’The point about the Epimenides, as was noted by Church in [1], is not that when we examine the truth value of a Cretan's assertion that nothing true is ever asserted by a Cretan we are led to contradictory conclusions, for we are not; the paradox is rather that such examination makes it seem possible to settle an empirical question on logical grounds. If we treat the Cretan's assertion as true, and so assume that nothing true is ever asserted by a Cretan, it follows immediately that the Cretan's assertion is false. If, however, we treat it as false, there is no way of deducing from this assumption that it is true. We can, therefore, consistently suppose it to be false, and this is all that we can consistently suppose. But to suppose it false (considering what the assertion actually is) is to suppose that something asserted by a Cretan is true; and this of course can only be some other assertion than the one mentioned. We thus reach the peculiar conclusion that if any Cretan does assert that nothing asserted by a Cretan is true, then this cannot possibly be the only assertion made by a Cretan — there must also be, beside this false Cretan assertion, some true one.
On Słupecki T-functions
Authors: Evans Trevor , Schwartz P. B. 
Published: May 2006

In [2] E. L. Post defined a many-valued propositional logic to be functionally complete if, for every function on the set of truth-values, there exists a formula of the logic having that function as its associated truth-value function. He proved that the logic with truth-values 1, 2, …, m and (i) a unary connective ∼ such that ∼p has truth-value i+1 (mod m) when p has truth-value i, (ii) a binary connective ∨ such that p ∨ q has truth-value min(i, j) when p, q have truth-values i, j respectively, is functionally complete.The many-valued logics described by Łukasiewicz and Tarski [1] are not functionally complete. These logics have truth-values 1, 2, …, m and (i) a unary connective ~ such that ~p has truth-value m−i+1 when p has truth-value i, (ii) a binary connective → such that if p, q have truth-values i, j respectively, then p → q has truth-value 1 for i ≧ j, and truth-value 1 for i ≧ j. The functional incompleteness of these logics is immediate, since there exists no formula in p having truth-value i (≠ 1 or m) when p has truth-value 1.In [4] Słupecki showed that if a new unary connective T, such that T(p) has truth-value 2 for all truth-values assigned to p, is added to the 3-valued Łukasiewicz-Tarski logic, then the resulting logic is functionally complete. In [3] Rosser and Turquette proved this result for the m-valued (m ≧ 3) logic.
Elite Recruitment and Political Leadership
Authors: Fukai Shigeko N. , Fukui Haruhiro 
Published: May 2006

Why should one study elite recruitment and political leadership in Japan? Because, our answer would go, we live in a world of ever deepening interdependence among nations where the peace, security, and prosperity of each is greatly influenced by policies and actions of another. This is particularly true when the latter is an economic superpower like Japan, the largest creditor nation and aid donor in the world of the early 1990s with a gross national product equal to about fifteen per cent of the world's total. Who makes Japanese domestic and foreign policies and how they are made has important implications for the welfare of other nations, including the United States, which maintains what a former American ambassador to Japan, Mike Mansfield, called the “most important bilateral relationship” in the world.“Elite” and “leadership” are two concepts that help us identify and analyze those who play central roles in a nation's policymaking process. Commonplace as they are in the vocabulary of both modern political science and the mass media, these words are often used ambiguously and interchangeably. They are, however, etymologically distinctive words that can serve us as useful analytical tools only if they are clearly and distinctively defined. In the discussion that follows, we use “elite” to refer to a group of individuals who hold privilegedpositionsin society or organizations and “leadership” to refer to theexerciseof power, broadly defined, to lead others in collective action. As William Welsh has suggested, elites are thus “set apart from the rest of society by their preeminence in political and governmental hierarchies,” while leadership means “ability to mobilize human resources in pursuit of specific goals.”
Asking Better Questions: The Problems of Constitutional Theory
Authors: Graber Mark A. 
Published: May 2006

Recently, some members of the public law subfield have begun exploring American constitutionalism in ways that may sound strange, if not perverse, to the uninitiated. Panels and papers are devoted to such topics as What is the Constitution? and Can there be unconstitutional constitutional amendments? Although confusing to some academics, these novel approaches to standard academic pursuits are also opening new lines of scholarly inquiry and unearthing doubtful assumptions that have gone unchallenged for too long. By laying out the new questions that political scientists are asking and could ask about constitutional theory, this paper may provide a guide for the perplexed and directions for future research.Throughout most of the twentieth century, the question, How should judges interpret the Constitution? was the central focus of constitutional theory. This inquiry conflated at least two distinct issues and, in so doing, ruled out legitimate constitutional possibilities. Because legal commentators failed to discriminate between theories about what the Constitution means and theories about how a particular institution, the judiciary, should resolve constitutional controversies, they normally assumed without question that the fundamental principles of the Constitution are judicially enforceable and that the judiciary is the authoritative interpreter of the Constitution.
Political Consultants: Opening Up a New System of Political Power
Authors: Lake Celinda 
Published: May 2006

I would like to address the question of whether having consultants opens up or closes up the political system. I am principally interested in the election of women and minority candidates. I work now for a firm where half of our candidates are women, which is a very high proportion. On the one hand consultants reinforce incumbency because there is such a strong relationship between money and being able to hire a consultant. By the same token I think that consultants have opened up the process of running for election.Recruitment of CandidatesWhen everyone talks about the decline of parties that means there are alternative routes to power, there are alternative routes to the skills that you need to get elected, and there are alternative routes to information. This has caused a major breakdown in political machines. Consultants are also aware of the different traits that can make people electable. Consultants first understood that there are certain districts where women candidates run better than male candidates, where women start out ahead because of the demographics of those districts. That is something that a male-dominated machine, for example, might resist but a consultant would relish and approach pragmatically. You also see outsiders with personal resources who have the most access to an alternative way of entering the system. The Wisconsin Democratic Senate race is a prime example of what can happen when a candidate with tremendous personal resources can hire a team and become a front-runner against people who have been running and elected for a long time.
Political Censorship: A Different View
Authors: Weissberg Robert 
Published: May 2006

The 1988 Winter PS contained five essays on textbook censorship. Though they covered a wide variety of topics, they shared a common and very familiar theme. Basically, in one form or another, they depicted and deplored right wing attempts to shape textbooks content and school adoption. O'Connor and Ivers, for example, described the fundamentalist attack on evolution and its advocacy of creationism. Adler discusses how the liberal People For the American Way had led the “counterattack” against organizations such as the Educational Research Analysts, a Texas based group worried about the lack of moral absolutes in sociology textbooks.To anyone acquainted with intellectual censorship, these tales are yet additional items to be added to thousands just like them. Indeed, there is such regularity to these stories that one might even formulate a near-universal generic school textbook censorship story: truth-seeking textbook author rejected by established publishers as too “controversial” eventually gets book into print but fails anyway due to pressure from intimidating right-wingers cloaked in the mantle of traditional American values. Intolerant jingoism again defeats truth.These PS articles no doubt paint an accurate picture of political pressure on textbooks. But, they present only a part of the story. They tell us nothing about the pressures on the textbook writer, pressures quite different than the familiar right wing “truth squads” hounding moral relativism from subversive tracts. As one who has written a text-Understanding American Government (Random House)—with separate college and high school editions, I have some experiences in this matter.
Politics Beyond The End of Liberalism
Authors: Petracca Mark P. 
Published: May 2006

The End of Liberalism is an ambitious, engaging, and intellectually provocative work even if it is also occasionally ambiguous, ahistorical, assuming, and utopian. This work attempts to build a theory of the modern American political regime which captures its complexity, inherent contradictions, institutional dilemmas, and self-destructive public philosophy. Since America has yet to abandon the politics and public philosophy of interest group liberalism, Theodore Lowi's (1969 and 1979) polemic remains a useful and now comfortable perch from which to observe the continuing crisis of public authority and shout appropriate epitaphs. There is little doubt that The End of Liberalism continues to stimulate, define, and inform intellectual and political debate in America 20 years after its initial publication.There are two ironies about The End of Liberalism which are now apparent two decades after its publication. First, if Lowi's work had been completely successful in laying to rest the demon of interest group liberalism and its spiritual compatriots, we might not be assessing the longevity and influence of this work two decades later.
Liberalism and Juridical Democracy, or What's Interesting About Interest Group Liberalism
Authors: Spitzer Robert J. 
Published: May 2006

Why is The End of Liberalism important? This work is not without its flaws or critics, but it is indisputably important—not because it is right, although I believe it largely is—but because it is provocative, stimulating, and pertinent to both scholai and practitioner.The CulpritOne of the more revealing and less pedantic kiss-and-tell books to come out of a presidential administration was David Stockman's (1987) The Triumph of Politics. In it, Stockman detailed his dismay over the failure of the Reagan Revolution—an effort to establish “minimalist government” (p. 9) incorporating “sweeping, wrenching change” that “would have hurt millions of people” (p. 11) by such actions as “elimination of subsidies to farmers and businesses … an immediate end to welfare for the able-bodied poor … [and] no right to draw more from the Social Security fund than retirees had actually contributed” (p. 12).
Text-Oriented Database Management
Authors: Permaloff Anne , Grafton Carl 
Published: May 2006

The management of large amounts of data is an important part of many research efforts. Quantitative data are inputted, stored, manipulated, and analyzed using such familiar tools as spreadsheets, database management programs like dBASE or Paradox, and statistics packages. However, some text based data such as bibliographies, text for content analysis, committee hearing transcripts, and historical information are not easily processed using such software. Statistics packages can handle only single words as string variables, and spreadsheets can usefully manage only short segments of text. Traditional database management programs can store and manipulate longer text segments, but many are limited to roughly three lines of text per entry or field unless they have a feature called a memo field to be discussed below.When we covered this topic for PS three years ago, we concluded that high end word processing packages should be considered first by most scholars who work with text data. We noted that advanced word processors contain search and sort capabilities that may be sufficient for many needs.