On a certain class ofm-address machines

Conclusion It follows from the proved theorems that ifM =Q, (whereQ={0,q ₁,q ₂,...,q }) is a machine of the classM _F then there exist machinesM _i such thatM _i(1,c)=M (q _i,c) andQ _i={0, 1, 2, ..., +1} (i=1, 2, ..., ).And thus, if the way in which to an initial function of content of memorycC a machine assigns a final onecC is regarded as the only essential property of the machine then we can deal with the machines of the formM ={0, 1, 2, ..., }, and processes (t) (wheret=1,c,cC) only.Such approach can simplify the problem of defining particular machines of the classM _F , composing and simplifying them.Allatum est die 19 Januarii 1970     

Sprachverstehende maschinen

In this paper the author tries to disentangle some of the problems tied up in John Searle's famous Chinese-room-argument. In a first step to answer the question what it would be for a system to have not only syntax, but also semantics the author gives a brief account of the functioning of the language understanding systems (LUS) so far developed in the framework of AI research thereby making clear that systems like Winograd's SHRDLU are indeed doing little more than mere number crunching. But things would be entirely different, the author argues, if the database of a LUS were built up by the system itself via some perceptual component-at least, if this perceptual component had the capacity to distinguish objects having a certain property F from objects which do not. For in this case the system could store an internal representation of the fact that the object has the property F in its database if and only if the object in fact has that property. And this would be a good basis for calling such a system a genuine LUS. But Searle has objected to a very similar account of J. Fodor that nothing could be further from true language understanding. The reason for this complaint seems to be that Searle holds the view that a true LUS must e.g., know that the word hamburgers refers to hamburgers and that he moreover claims that this knowledge must be explicit or that the system must be aware of the reference of hamburgers to hamburgers. The author argues that this is asking too much. For it seems plausible to say that a system is able to understand e.g., the word hamburger even if it has only implicit knowledge of the fact that hamburger refers to hamburgers in the sense that it has the capacity to tell hamburgers from non hamburgers and the capacity to bring the word hamburger together just with objects of the former kind.     

A cut-free gentzen-type system for the logic of the weak law of excluded middle

The logic of the weak law of excluded middleKC _p is obtained by adding the formula A A as an axiom scheme to Heyting's intuitionistic logicH _p . A cut-free sequent calculus for this logic is given. As the consequences of the cut-elimination theorem, we get the decidability of the propositional part of this calculus, its separability, equality of the negationless fragments ofKC _p andH _p , interpolation theorems and so on. From the proof-theoretical point of view, the formulation presented in this paper makes clearer the relations betweenKC _p ,H _p , and the classical logic. In the end, an interpretation of classical propositional logic in the propositional part ofKC _p is given.     

Intensional Completeness in an Extension of Gödel/Dummett Logic

We enrich intuitionistic logic with a lax modal operator and define a corresponding intensional enrichment of Kripke models M = (W, , V) by a function T giving an effort measure T(w, u) {} for each -related pair (w, u). We show that embodies the abstraction involved in passing from true up to bounded effort to true outright. We then introduce a refined notion of intensional validity M |= p : and present a corresponding intensional calculus iLC-h which gives a natural extension by lax modality of the well-known G: odel/Dummett logic LC of (finite) linear Kripke models. Our main results are that for finite linear intensional models L the intensional theory iTh(L) = {p : | L |= p : } characterises L and that iLC-h generates complete information about iTh(L).Our paper thus shows that the quantitative intensional information contained in the effort measure T can be abstracted away by the use of and completely recovered by a suitable semantic interpretation of proofs.     

A note on the equivalence of the graded response model and the sequential model

This paper concerns items that consist of several item steps to be responded to sequentially. The item scoreX is defined as the number of correct responses until the first failure. Samejima's graded response model states that each steph=1,...,m is characterized by a parameterb _h , and, for a subject with ability, Pr(Xh; )=F(–b _h ). Tutz's general sequential model associates with each step a parameterdh, and it states that Pr(Xh;)= _r ^=1h G(–d _r ). Tutz's (1991, 1997) conjectures that the models are equivalent if and only ifF(x)=G(x) is an extreme value distribution. This paper presents a proof for this conjecture.     

A pragmatic interpretation of intuitionistic propositional logic

We construct an extension ^P of the standard language of classical propositional logic by adjoining to the alphabet of a new category of logical-pragmatic signs. The well formed formulas of are calledradical formulas (rfs) of ^P;rfs preceded by theassertion sign constituteelementary assertive formulas of ^P, which can be connected together by means of thepragmatic connectives N, K, A, C, E, so as to obtain the set of all theassertive formulas (afs). Everyrf of ^P is endowed with atruth value defined classically, and everyaf is endowed with ajustification value, defined in terms of the intuitive notion of proof and depending on the truth values of its radical subformulas. In this framework, we define the notion ofpragmatic validity in ^P and yield a list of criteria of pragmatic validity which hold under the assumption that only classical metalinguistic procedures of proof be accepted. We translate the classical propositional calculus (CPC) and the intuitionistic propositional calculus (IPC) into the assertive part of ^P and show that this translation allows us to interpret Intuitionistic Logic as an axiomatic theory of the constructive proof concept rather than an alternative to Classical Logic. Finally, we show that our framework provides a suitable background for discussing classical problems in the philosophy of logic.This paper is an enlarged and entirely revised version of the paper by Dalla Pozza (1991) worked out in the framework of C.N.R. project n. 89.02281.08, and published in Italian. The basic ideas in it have been propounded since 1986 by Dalla Pozza in a series of seminars given at the University of Lecce and in other Italian Universities. C. Garola collected the scattered parts of the work, helped in solving some conceptual difficulties and refining the formalism, yielded the proofs of some propositions (in particular, in Section 3) and provided physical examples (see in particular Remark 2.3.1).     

On a new property of partially balanced association schemes useful in psychometric structural analysis

In an earlier paper [Psychometrika,31, 1966, p. 147], Srivastava obtained a test for the HypothesisH ₀ : = ₀₀ + ... + _ll, where i are known matrices,i are unknown constants and is the unknown (p ×p) covariance matrix of a random variablex (withp components) having ap-variate normal distribution. The test therein was obtained under (p ×p) covariance matrix of a random variablex (withp components) the condition that ₀, ₁, ..., l form a commutative linear associative algebra and a certain vector, dependent on these, has non-negative elements. In this paper it is shown that this last condition is always satisfied in the special situation (of importance in structural analysis in psychometrics) where ₀, ₁, ..., l are the association matrices of a partially balanced association scheme.This research was partially supported by the U. S. Air Force under Grant No. AF33(615)-3231, monitored by the Aero Space Research Labs.Now at Colorado State University.     

The American plan completed: Alternative classical-style semantics,without stars,for relevant and paraconsistent logics

American-plan semantics with 4 values 1, 0, { {1, 0}} {{}}, interpretable as True, False, Both and Neither, are furnished for a range of logics, including relevant affixing systems. The evaluation rules for extensional connectives take a classical form: in particular, those for negation assume the form 1 (A, a) iff 0 (A, a) and 0 (A, a) iff 1 (A, a), so eliminating the star function *, on which much criticism of relevant logic semantics has focussed. The cost of these classical features is a further relation (or operation), required in evaluating falsity assignments of implication formulae.Two styles of 4 valued relational semantics are developed; firstly a semantics using notions of double truth and double validity for basic relevant systemB and some extensions of it; and secondly, since the first semantics makes heavy weather of validating negation principles such as Contraposition, a reduced semantics using more complex implicational rules for relevant systemC and various of its extensions. To deal satisfactorily with elite systemsR,E andT, however, further complication is inevitable; and a relation of mateship (suggested by the Australian plan) is introduced to permit cross-over from 1 to 0 values and vice versa.     

The relative consistency of system RRC* and some of its extensions

We present a relative consistency proof for second order systemRRC* and for certain important extensions of this system. The proof proceeds as follows: we prove first the equiconsistency of the strongest of such extensions (viz., systemH RRC*+(/CP**)) with second order systemT ^* . Now, N. Cocchiarella has shown thatT ^* is relatively consistent to systemT*+Ext; clearly, it follows thatH RRC*+(/CP**) is relatively consistent toT*+E _xt. As an immediate consequence, the relative consistency ofRRC* and the other extensions also follows, being all of them subsystems ofH RRC*+(/CP**).I am grateful to the referee for some modifications suggested to an earlier draft of this paper.Presented byMelvin Fitting     

Completeness theorem for dummett's LC quantified and some of its extensions

Dummett's logic LC quantified, Q-LC, is shown to be characterized by the extended frame Q⁺, ,D, where Q⁺ is the set of non-negative rational numbers, is the numerical relation less or equal then and D is the domain function such that for all v, w Q⁺, D_v and if v w, then D _v . D _v D _w . Moreover, simple completeness proofs of extensions of Q-LC are given.     

Supererogation in Deontic Logic: Metatheory for DWE and Some Close Neighbours

In "Doing Well Enough: Toward a Logic for Common Sense Morality", Paul McNamara sets out a semantics for a deontic logic which contains the operator It is supererogatory that. As well as having a binary accessibility relation on worlds, that semantics contains a relative ordering relation, . For worlds u, v and w, we say that u w v when v is at least as good as u according to the standards of w. In this paper we axiomatize logics complete over three versions of the semantics. We call the strongest of these logics DWE for Doing Well Enough.     

Maximization of sums of quotients of quadratic forms and some generalizations

Monotonically convergent algorithms are described for maximizing six (constrained) functions of vectors x, or matricesX with columns x₁, ..., x _r . These functions are h₁(x)= _k (xA _kx)(xC _kx)^–1, H₁(X)= _k tr (XA _k X)(XC _k X)^–1, h₁(X)= _{k l} (x _l A _kx _l ) (x _l C _kx _l )^–1 withX constrained to be columnwise orthonormal, h₂(x)= _k (xA _kx)²(xC _kx)^–1 subject to xx=1, H₂(X)= _k tr(XA _kX)(XA_kX)(XC_kX)^–1 subject toXX=I, and h₂(X)= _{k l} (x _l A _kx _l )² (x _l C _kX _l )^–1 subject toXX=I. In these functions the matricesC _k are assumed to be positive definite. The matricesA _k can be arbitrary square matrices. The general formulation of the functions and the algorithms allows for application of the algorithms in various problems that arise in multivariate analysis. Several applications of the general algorithms are given. Specifically, algorithms are given for reciprocal principal components analysis, binormamin rotation, generalized discriminant analysis, variants of generalized principal components analysis, simple structure rotation for one of the latter variants, and set component analysis. For most of these methods the algorithms appear to be new, for the others the existing algorithms turn out to be special cases of the newly derived general algorithms.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the author. The author is obliged to Jos ten Berge for stimulating this research and for helpful comments on an earlier version of this paper.     

The logical structure of linguistic commitment II: Systems of relevant commitment entailment

In The Logical Structure of Linguistic Commitment I (The Journal of Philosophical Logic 23 (1994), 369–400), we sketch a linguistic theory (inspired by Brandom's Making it Explicit) which includes an expressivist account of the implication connective, : the role of is to make explicit the inferential proprieties among possible commitments which proprieties determine, in part, the significances of sentences. This motivates reading (A B) as commitment to A is, in part, commitment to B. Our project is to study the logic of . LSLC I approximates (A B) as anyone committed to A is committed to B, ignoring issues of whether A is relevant to B. The present paper includes considerations of relevance, motivating systems of relevant commitment entailment related to the systems of commitment entailment of LSLC I. We also consider the relevance logics that result from a commitment reading of Fine's semantics for relevance logics, a reading that Fine suggests.     

On Łukasiewicz-Moisil algebras of fuzzy sets

The set (X, J) of fuzzy subsetsf:XJ of a setX can be equipped with a structure of -valued ukasiewicz-Moisil algebra, where is the order type of the totally ordered setJ. Conversely, every ukasiewicz-Moisil algebra — and in particular every Post algebra — is isomorphic to a subalgebra of an algebra of the form (X, J), whereJ has an order type . The first result of this paper is a characterization of those -valued ukasiewicz-Moisil algebras which are isomorphic to an algebra of the form (X, J) (Theorem 1). Then we prove that (X, J) is a Post algebra if and only if the setJ is dually well-ordered (Theorem 2) and we give a characterization of those -valued Post algebras with are isomorphic to an algebra of the form (X, J) (Theorem 3 and Proposition 2).     

Rules in relevant logic — II: Formula representation

This paper surveys the various forms of Deduction Theorem for a broad range of relevant logics. The logics range from the basic system B of Routley-Meyer through to the system R of relevant implication, and the forms of Deduction Theorem are characterized by the various formula representations of rules that are either unrestricted or restricted in certain ways. The formula representations cover the iterated form,A ₁ .A ₂ . ... .A _n B, the conjunctive form,A ₁&A ₂ & ...A _n B, the combined conjunctive and iterated form, enthymematic version of these three forms, and the classical implicational form,A ₁&A ₂& ...A _n B. The concept of general enthymeme is introduced and the Deduction Theorem is shown to apply for rules essentially derived using Modus Ponens and Adjunction only, with logics containing either (A B)&(B C) .A C orA B .B C .A C.I acknowledge help from anonymous referees for guidance in preparing Part II, and especially for the suggestion that Theorem 9 could be expanded to fully contraction-less logics.     

Parameter estimation in latent trait models

Latent trait models for binary responses to a set of test items are considered from the point of view of estimating latent trait parameters=( ₁, , _n ) and item parameters=( ₁, , _k ), where _j may be vector valued. With considered a random sample from a prior distribution with parameter, the estimation of (, ) is studied under the theory of the EM algorithm. An example and computational details are presented for the Rasch model.This work was supported by Contract No. N00014-81-K-0265, Modification No. P00002, from Personnel and Training Research Programs, Psychological Sciences Division, Office of Naval Research. The authors wish to thank an anonymous reviewer for several valuable suggestions.     

Three prepositional calculi of probability

Attempts are made to transform the basis of elementary probability theory into the logical calculus.We obtain the propositional calculus NP by a naive approach. As rules of transformation, NP has rules of the classical propositional logic (for events), rules of the ukasiewicz logic ₀ (for probabilities) and axioms of probability theory, in the form of rules of inference. We prove equivalence of NP with a fragmentary probability theory, in which one may only add and subtract probabilities.The second calculus MP is a usual modal propositional calculus. It has the modal rules x x, x y x y, x x, x y (y x), (y x), in addition to the rules of classical propositional logic. One may read x as x is probable. Imbeddings of NP and of ₀ into MP are given.The third calculus P is a modal extension of ₀. It may be obtained by adding the rule ((xy)y) xy to the modal logic of quantum mechanics Q [5]. One may read x in P as x is observed. An imbedding of NP into P is given.     

The varying presuppositional nature of comparatives

The presuppositional nature of different types of comparatives was studied by obtaining subjects' judgments concerning the synonymity of pairs of comparative statements and the acceptability of single comparative statements. The results indicated that, in general, significantly greater presupposition was involved in the negative comparatives (e.g.,Bob is not as large as Fred) than in the positive comparatives (e.g.,Fred is larger than Bob), in the extreme comparatives (e.g.,Fred is more saintly than Bob) than in the regular comparatives (e.g.,Fred is better than Bob), in the ordinal comparatives (e.g.,Bob is more agile than Fred) than in the ratio comparatives (e.g.,Bob is heavier than Fred), and in the marked comparatives (e.g.,Bob is worse than Fred) than in the unmarked comparatives (e.g.,Fred is better than Bob). The results also indicated that comparative statements containing marked adjectives from a ratio scale can be interpreted neutrally. The implications of these results for the linguistic distinction between marked and unmarked adjectives are discussed. Presuppositions were found to apply equally to the subject and object terms of a comparative statement. In general, the results suggest that presuppositional effects are quite systematic and accumulative in nature.     

Nietzsche's agon with ressentiment: towards a therapeutic reading of critical transvaluation

This paper examines the therapeutic implications of Nietzsche's critique of ressentiment and revenge as our signature malady. §I examines the obstacles to a therapeutic reading of Nietzsche's thought, including his anti-teleological tendencies and the value he places on sickness. Then there is the energetic problem of finding resources to tackle ressentiment, given the volitional exhaustion of modern nihilism. Finally, the self-referential implications of Nietzsche's critique of slave values threaten to trap his thought in a futile ressentiment against ressentiment. If the impulse to cure or redeem us from revenge through critical destruction repeats the logic of revenge, then the challenge for a therapeutic reading is to think through the transformation of revenge on the basis of repetition.An agonal reading of Nietzsche's philosophical practice is proposed to tackle these problems in §II.In Homer's Contest (1872), Nietzsche describes the transference (Übertragung) of Hesiod's evil Eris – goddess of war and destruction – into the good Eris of the contest or agon: destructive impulses are affirmed as stimulants, but also transformed into culture-building forces through an agonal regime of limited aggression. By superimposing this regime, as a model for Nietzsche's textual confrontations, on their unconscious text of embodied ressentiment, a therapeutic perspective emerges, based on three principles: affirmation; mutual empowerment; and externalisation. The agon performs an affirmative transformation of revenge on the basis of a fertile repetition: destructive affects (as in ressentiment) are transferred into constructive deeds of mutual antagonism. Through Nietzsche's agonal discourse, a reactive regime of internalised aggression is externalised in active deeds of limited philosophical aggression – a therapeutic transformation of (self-)destructive into constructive, philosophical impulses.