Pure Logic Research Articles

Probability Measures in the Logic of Nilpotent Minimum

We axiomatize the notion of state over finitely generated free NM-algebras, the Lindenbaum algebras of pure Nilpotent Minimum logic. We show that states over the free n-generated NM-algebra \({{\fancyscript{NM}_{n}}}\) exactly correspond to integrals of elements of \({{\fancyscript{NM}_{n}}}\) with respect to Borel probability measures.

Is observational congruence on [formula omitted]-expressions axiomatisable in equational Horn logic?

It is well known that bisimulation on μ -expressions cannot be finitely axiomatised in equational logic. Complete axiomatisations such as those of Milner and Bloom/Ésik necessarily involve implicational rules. However, both systems rely on features beyond pure equational Horn logic: either rules that are impure by involving non-equational side-conditions, or rules that are schematically infinitary like the congruence rule which is not Horn. It is an open question whether these complications cannot be avoided in the proof-theoretically and computationally clean and powerful setting of second-order equational Horn logic. This paper presents a positive and a negative result regarding the axiomatisability of observational congruence in equational Horn logic. Firstly, we show how Milner’s impure rule system can be reworked into a pure Horn axiomatisation that is complete for guarded processes. Secondly, we prove that for unguarded processes, both Milner’s unique fixed point rule and Bloom/Ésik’s GA rule are incomplete without the congruence rule, and neither system has a complete extension in rank-1 equational axioms. It remains open whether there are higher-rank equational axioms or other Horn rules which would render Milner’s or Bloom/Ésik’s axiomatisations complete.

Temporal Logics of Agency

Time is the grand stage where human activities take place (rational or otherwise). And the view of a branching temporal universe, or tree of possible events, with our actual history linearly advancing through it, is a widely shared cultural idea, not confined to Academia (cf. Borges brilliant 1941 essayEl Jardin de senderos que se bifurcan). Even though logic is often considered a study of timeless propositions, temporal languages and logics over tree structures have a long tradition. Philosophers have studied temporal structure and temporal reasoning since the 1950s, from the ‘tense logic’ of Prior (1967) to the ‘STIT’ system of Belnap et al. (2001). Moreover, starting from 1970s, computer scientists have joined in, and developed many further flavours of temporal logic, with major strands such as Pnueli on program correctness (Manna and Pnueli 1991), Emerson and Clarke on process specification and verification (Emerson and Clarke 1980, 1982), Reiter on the situation calculus in AI (Reiter 2001), and Thomas on the automata-theoretic foundations of computing (Thomas 1990). In addition, the pure firstand second-order logic of tree-like structures, starting from Rabin’s classic decidability result (Rabin 1969), provides deeper background (cf. Gradel et al. (2002)). The chapter by Hodkinson and Reynolds on ‘Temporal Logic’ in the Handbook of Modal Logic (Hodkinson and Reynolds 2006) brings together many of these trends in one mathematical narrative. But the field of reasoning in, and about, time can be mapped out in many further ways: Van Benthems chapter ‘Temporal Logic’ in the

O projeto fenomenológico de fundação das ciências

Em primeiro lugar, este artigo esclarece que o sentido de fundação das ciências proposto por Husserl não deve ser confundido com algum tipo de fundacionismo epistêmico (seção 1). Em seguida, expõe o primeiro modelo de fundação do conhecimento defendido por Husserl, em Filosofia da aritmética, e as principais críticas recebidas (seções 2-3). Por fim, acompanha a elaboração de um segundo modelo, apresentado em Prolegômenos à lógica pura (seções 4-7).

Eskolemization in Intuitionistic Logic

In Baaz and Iemhoff (2006, Annals of Pure and Applied Logic, 142, 269–295), an alternative skolemization method called eskolemization was introduced that is sound and complete for existence logic with respect to existential quantifiers. Existence logic is a conservative extension of intuitionistic logic by an existence predicate. Therefore, eskolemization provides a skolemization method for intuitionistic logic as well. All proofs in Baaz and Iemhoff (2006, Annals of Pure and Applied Logic, 142, 269–295) were semantical. In this article, a proof-theoretic proof of the completeness of eskolemization with respect to existential quantifiers is presented.

L 009 Variables Related to Changes in Plasma Levels of Triglycerides and Fasting Blood Glucose After Short-term Red Wine Intake

This volume contains the Proceedings of the 9th Workshop on Logic, Language, Information and Computation (WoLLIC'2002). The Workshop was held in Rio de Janeiro, Brazil from July 30 to August 2, 2002, in the campus of the Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio).WoLLIC is a series of workshops which started in 1994 with the aim of fostering interdisciplinary research in pure and applied logic. The idea is to have a forum which is large enough in the number of possible interactions between logic and the sciences related to information and computation, and yet is small enough to allow for concrete and useful interaction among participants. Previous versions were held at: Recife (Pernambuco, Brazil) in 1994 and 1995; Salvador (Bahia, Brazil) in 1996; Fortaleza (Ceará, Brazil) in 1997; São Paulo (Brazil) in 1998; Itatiaia (Rio de Janeiro, Brazil) in 1999; Natal (Rio Grande do Norte) in 2000; Brasília (Distrito Federal, Brazil) in 2001. [new] Scientific sponsorship comes from the Interest Group in Pure and Applied Logics (IGPL), the European Association for Logic, Language and Information (FoLLI), the Association for Symbolic Logic (ASL), the Sociedade Brasileira de Computação (SBC), and the Sociedade Brasileira de Lógica (SBL).[end new] Scientific sponsorship comes from the Interest Group in Pure and Applied Logics (IGPL), the European Association for Logic, Language and Information (FoLLI), the Association for Symbolic Logic (ASL), the Sociedade Brasileira de Computação (SBC), and the Sociedade Brasileira de Lógica (SBL). Funding was kindly given by: (i) CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico, the scientific and technological development council of the Brazilian Ministério da Ciência e Tecnologia) (grant 451491/2002-5); (ii) CAPES (Fundação Coordenação de Apoio ao Aperfeiçoamento de Pessoal de Nível Superior, a Foundation for the Development of Higher-Education under the Brazilian Ministério da Educação e do Desporto) (grant PAEP0169/02-1); (iii) PUC-Rio (Pontifícia Universidade Católica do Rio de Janeiro). Contributions were received in the form of short papers in all areas related to logic, language, information and computation, including: pure logical systems, proof theory, model theory, algebraic logic, type theory, category theory, constructive mathematics, lambda and combinatorial calculi, program logic and program semantics, logics and models of concurrency, logic and complexity theory, proof complexity, foundations of cryptography (zero-knowledge proofs), descriptive complexity, nonclassical logics, nonmonotonic logic, logic and language, discourse representation, logic and artificial intelligence, automated deduction, foundations of logic programming, logic and computation, and logic engineering.Apart from the contributed papers (14), and the invited talks (6), the programme includes 6 tutorial lectures: •Some model theory of ordered structures by Ricardo Bianconi (Departamento de Matemática Pura, Instituto de Matemática e Estatística, Universidade de São Paulo, Brazil)•Computing with Real Numbers by Felipe Cucker (Department of Mathematics, City University of Hong Kong, People's Republic of China)•Model Checking Games by Erich Grädel (Mathematische Grundlagen der Informatik, RWTH Aachen, Germany)•The Metalanguage Lambda Prolog and its Implementation by Gopalan Nadathur (University of Minnesota, USA)•Automata theory and logic by Igor Walukiewicz (Bordeaux University, France)•States of Knowledge (Tutorial) by Rohit Parikh (Department of Computer and Information Science, Brooklyn College, City University of New York, USA)All papers in the volume were reviewed by the program committee consisting, besides editor, of The organising committee consisted, besides editor, of The volume will be published as volume 67 in the series Electronic Notes in Theoretical Computer Science (ENTCS). This series is published electronically through the facilities of Elsevier Science B.V. and its auspices. The volumes in the ENTCS series can be accessed at the URL http://www.elsevier.nl/locate/entcsA printed version of the current volume is distributed to the participants at the workshop in Rio de Janeiro.We are very grateful to the following persons, whose help has been crucial for the success of WoLLIC'2002: Mike Mislove, one of the Managing Editors of the ENTCS series, for his assistance with the use of the ENTCS style files; Thanks are also due to the Departments of Philosophy and Informatics of the Pontifícia Universidade Católica of Rio de Janeiro, which has provided the logistic support to the organising committee.July 26, 2002 Ruy de Queiroz

A study of gateless OTP cell using a 45 nm CMOS compatible process

This work proposes a new gateless one-time programmable (OTP) cell. This gateless OTP cell has a parasitic oxide–nitride–oxide (ONO) structure as the storage node and is successfully demonstrated in a 45 nm CMOS logic process. This gateless OTP cell, formed in a pure logic process and decoupled from gate oxide, is highly stable with a five orders of on/off current window. It also exhibits superior program performance, with an operating voltage of only 5 V and at a programming current of no more than 10 μA. Unlike breakdown-based anti-fuses, electron trapping of the gateless OTP cell demonstrates repeatability for testing. The gateless OTP can be UV-erased and is stable over 10 P/E cycles. An electrical erase mechanism with limited performance is also characterized and discussed. This new nitride gateless anti-fuse cell is a very promising logic OTP solution that provides fully compatibility to CMOS process below the 90 nm node.

Julius Konig et les Principes Aristoteliciens

In his posthumous book from 1914, New foundations of logic, arithmetic and set theory, Julius Konig develops his philosophy of mathematics. In a previous contribution, we attracted attention on the positive part (his truth and falsehood predicates being excluded) of his pure logic: his isology being assimilated to mutual implication, it constitutes a genuine formalization of positive intuitionistic logic. Konig's intention was to rebuild logic in such a way that the excluded third's principle could no longer be logical. However, his treatment of truth and falsehood (boiling down to negation) is purely classical. We explain here this discrepancy by the choice of the alleged more primitive notions to which the questioned notions of truth and falsehood have been reduced. Finaly, it turns out that the disjunctive and conjunctive forms of the principles of the excluded third and of contradiction have effectively been excluded, but none of their implicative forms.

Magnetic logic using nanowires with perpendicular anisotropy

In addition to a storage function through the magnetization of nanowires, domain wallpropagation can be used to trigger magnetic logic functions. Here, we present anew way to realize a pure magnetic logic operation by using magnetic nanowireswith perpendicular anisotropy. Emphasis is given on the generation of the logicfunction ‘NOT’ that is based on the dipolar interaction between two neighbouringmagnetic wires, which favours the creation of a domain wall. This concept has beenvalidated on several prototypes and the results fit well with the expectations.

The Role of Empirical Assumptions in Economic Analysis: On Facts and Counterfactuals in Economic Law

How much of economic theory can be derived using pure logic and how much of it depends on empirical facts? In a provocative article, Hülsmann (2003) criticizes Mises and Rothbard for relying on empirical assumptions, ceteris paribus claims, and thought experiments in their analysis. Instead, Hülsmann proposes a counterfactual method that does not rely on any empirical assumptions and is said to produce universally valid claims. Upon inspection we find that many of his proposed laws are either inexact, incorrect, or must rely on subsidiary assumptions to be true. We conclude that the traditional approach of Mises and Rothbard appears to be more fruitful and true.

Dictatorship, liberalism and the Pareto rule: Possible and impossible

The current economic crisis has shaken belief in the capacity of neoliberal 'free market' policies. Numerous supports of state intervention have arisen, and the interest for social choice theory has revived. In this paper we consider three standard properties for aggregating individual into social preferences: dictatorship, liberalism and the Pareto rule, and their formal negations. The context of the pure first-order classical logic makes it possible to show how some combinations of the above mentioned conditions, under the hypothesis of unrestricted domain, form simple and reasonable examples of possible or impossible social choice systems. Due to their simplicity, these examples, including the famous 'liberal paradox', could have a particular didactic value.

Od „Zarysu teorii nonsensu” do czystego nonsensu w życiu codziennym

Contrary to common conviction, which treats pure nonsense and logic as a relation of incompatibility and incongruity, it is the relation of contiguity that appears to be fundamental for the principle of the paralogic of pure nonsense. Like in the poetry of nonsense also even nonsensical jokes or absurd situations appear to be peculiarly logical (i.e. paralogical). Studies of metaphor and panegyric seem to be this trope, which most closely leads to the goal which is a theory of literature view of pure nonsense.

Judging by the Numbers: An Empirical Study of the Power of Story to Persuade (Test Briefs)

This document includes the test briefs sent to participants (appellate judges, law clerks, appellate lawyers and law professors) in a study of whether appellate briefs which include a strand of narrative reasoning are more persuasive than briefs which emphasize pure logic.

The Division of Action in Thomas Aquinas

Aquinas accepts that (i) some kinds of voluntary action are (qua voluntary) basic, not divisible into (non-fictional) further kinds; (ii) a concrete individual action may belong to more than one basic kind; (iii) the basic kinds to which it belongs are determined by the agent's intentions qua performing the action; (iv) some intentions may stand to others as means to ends; (v) there can be concrete individual actions in which the agent's intended means are disordered with respect to the ends; (vi) such actions are morally wrong; (vii) whether a given intention is disordered as means to a given end is determined solely by the natures of the agent and of the intended means or ends. Together, these propositions entail that, pace many analytic philosophers, concrete individual actions can have a moral wrongness that consists neither in expectation of disutility nor in violation of the pure logic of practical reason.

A Note on Expressive Coalgebraic Logics for Finitary Set Functors

This article has two purposes. The first is to present a final coalgebra construction for finitary endofunctors on Set that uses a certain subset L* of the limit L of the first ω terms in the final sequence. L* is the set of points in L which arise from all coalgebras using their canonical morphisms into L, and it was used earlier for different purposes in Kurz and Pattinson (2005, Mathematical Structures in Computer Science, 15, 543–473). Viglizzo (2005, PhD Dessertation, Indiana University) showed that the same set L* carried a final coalgebra structure for functors in a certain inductively defined family. Our first goal is to generalize this to all finitary endofunctors; the result is implicit in Worrell (2005, Theoritical Computer Science, 338, 184–199). The second goal is to use the final coalgebra construction to propose coalgebraic logics similar to those in Lawrence S. Moss (1999, Annals of Pure and Applied Logic, 96, 277–317) but for all finitary endofunctors F on Set. This time one can dispense with all conditions on F, construct a logical language LF directly from it, and prove that two points in a coalgebra satisfy the same sentences of LF iff they are identified by the final coalgebra morphism. The language LF is very spare, having no boolean connectives. This work on LF is thus a re-working of coalgebraic logic for finitary functors on sets.

On lengths of proofs in non-classical logics

We give proofs of the effective monotone interpolation property for the system of modal logic K , and others, and the system I L of intuitionistic propositional logic. Hence we obtain exponential lower bounds on the number of proof-lines in those systems. The main results have been given in [P. Hrubeš, Lower bounds for modal logics, Journal of Symbolic Logic 72 (3) (2007) 941–958; P. Hrubeš, A lower bound for intuitionistic logic, Annals of Pure and Applied Logic 146 (2007) 72–90]; here, we give considerably simplified proofs, as well as some generalisations.

On Oscillation-free ε-random Sequences

In this paper we discuss three notions of partial randomness or ε-randomness. ε-randomness should display all features of randomness in a scaled down manner. However, as Reimann and Stephan [J. Reimann, and F. Stephan, On hierarchies of randomness tests, in: Mathematical Logic in Asia, Proceedings of the 9th Asian Logic Conference, Novosibirsk, World Scientific, Singapore 2006] proved, Tadaki [K. Tadaki, A generalization of Chaitin's halting probability Ωand halting self-similar sets, Hokkaido Math. J. 31 (2002), 219–253] and Calude et al. [C.S. Calude, L. Staiger, and S.A. Terwijn. On partial randomness, Annals of Applied and Pure Logic, 138 (2006), 20–30] proposed at least three different concepts of partial randomness.We show that all of them satisfy the natural requirement that any ε-non-null set contains an ε-random infinite word. This allows us to focus our investigations on the strongest one which is based on a priori complexity.We investigate this concept of partial randomness and show that it allows—similar to the random infinite words—oscillation-free (w.r.t. to a priori complexity) ε-random infinite words if only ε is a computable number. The proof uses the dilution principle.Alternatively, for certain sets of infinite words (ω-languages) we show that their most complex infinite words are oscillation-free ε-random. Here the parameter ε is also computable and depends on the set chosen.

Development of a new minimum avoidance system for a behavior-based mobile robot

A new fuzzy logic algorithm is developed for mobile robot navigation in local environments. A Pioneer robot perceives its environment through an array of eight sonar sensors and self positioning-localization sensors. While the fuzzy logic body of the algorithm performs the main tasks of obstacle avoidance and target seeking, an actual–virtual target switching strategy resolves the problem of limit cycles in any type of dead-ends encountered on the way to the target. This is an advantage beyond pure fuzzy logic approach and common virtual target techniques. In this work, multiple traps may have any shape or arrangement from barriers forming simple corners and U-shape dead-ends to loops, maze, snail shape, and other complicated shapes. Robot trajectories are demonstrated by simulation work and compared with results from other related methods to prove the robustness of this method.

Notas acerca dos Pressupostos e Consequências da Críticaao Relativismo Nos Prolegómenos À Lógica Pura de Husserl

Abstract Notwithstanding its critical and refutative method and scope, which are so different from his subsequent phenomenological work, Husserl’s Prolegomena to Pure Logic lays the foundations for that later work. His refutation of relativism is based upon the existence of a general form for scientific “foundations”, the availability of non-linguistic evidence of pure significations and the possibility of the subject reflecting upon its own acts, which also pave the way for Phenomenology. This paper also points out that, although the later relativist philosophy often rested on exactly the opposite theses of the Prolegomena, the arguments of this work were not seriously discussed or refuted.

Fog forecasting using rule-based fuzzy inference system

Operational meteorology is perceived as a fuzzy environment in which information is vaguely defined. The mesoscale processes such as fog, stratus and convection are generally dependent on the topography of the place and has always been difficult to forecast for the meteorologists. The main objective of the present study is to introduce the concept of fuzzy inference system (FIS) in the prediction of fog. This approach uses the concept of a pure fuzzy logic system where the fuzzy rule base consists of a collection of fuzzy IF-THEN rules. The fuzzy inference engine uses these fuzzy IF-THEN rules to determine a mapping from fuzzy sets in the input universe of discourse to fuzzy sets in the output universe of discourse based on fuzzy logic principles. Basic weather elements, which affect weather characteristics of fog, are fuzzified. These are then used in fuzzy weather prediction models based on fuzzy inferences. These models are simulated and the crisp results obtained using developed defuzzification strategies are compared with the actual weather data. The basis of methodology is to construct the fuzzy rule base domain from the available daily current weather observations in winter season over New Delhi. The results reveal that dew point spread and rate of change of dew point spread are the most important parameters for the formation of fog. The results further indicate that fog formation over New Delhi are dominant when (i) dew point is greater then 7°C along with dew point spread between 1 and 3°C. (ii) rate of change of dew point spread must be negative and wind speed should be less than 4 knots. This study presents a technique for predicting the probability of fog over New Delhi for 5–6 hours in advance. The skill score indicates that the performance of FIS is appreciably good. The method is found to be promising for operational application.