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 L3, the intuitionistic system I1 and several paraconsistent logics, as for instance Sette's system P1, the D'Ottaviano and da Costa system J3 and da Costa's systems Cn, 1≤ n≤ω. (shrink)

A general mathematical framework, based on countable partitions of Natural Numbers [1], is presented, that allows to provide a Semantics to propositional languages. It has the particularity of allowing both the valuations and the interpretation Sets for the connectives to discriminate complexity of the formulas. This allows different adequacy criteria to be used to assess formulas associated with the same connective, but that differ in their complexity. The presented method can be adapted potentially infinite number of connectives and truth values, (...) therefore, it can be considered a general framework to provide semantics to several of the known logic systems (eg, LC, L3 LP, FDE). The presented semantics allow to converge to different standard semantics if the separation complexity procedure is annulled. Therefore, it can be understood as a framework that allows greater precision (in complexity terms) with respect to formula satisfaction. Naturally, because of how it is built, it can be incorporated into non-deterministic semantics. The presented procedure also allows generating valuations that grant a different truth value to each formula of propositional language. As a positive side effect, our method allows a constructive proof of the equipotence between N and N^n for all Natural n. (shrink)

In this paper I argue that logical multivalency is necessary for epistemology and has desirable structural properties. In support of this claim, I discuss the nonclassical logical values from an epistemological point of view. The question addressed is how many logical values logicians and philosophers need. Two standpoints are usually adopted regarding this issue: the fundamentality of bivalence and the necessity of multivalence. The first position, supported by Suszko, is summarized in the statement that due to the very nature of (...) logic, bivalency is all we need. The second position, motivated by research practice which requires making inferences under imperfect conditions, admits the multivalence. In the first part of the article, I focus on the very first manyvalued system L3, invented and explored by Jan Łukasiewicz. I recount the critique of L3, and then discuss Suszko’s thesis and Malinowski’s response. I also analyze the epistemological background of the Suszko-Łukasiewicz controversy which was related to the relation between logic, antirealism and externalism. I conclude fundamentalism regarding logical bivalence generates more problems than the adoption of multivalency. (shrink)

A recursively enumerable splitting of an r.e. setAis a pair of r.e. setsBandCsuch thatA=B∪CandB∩C= ⊘. Since for such a splitting degA= degB∪ degC, r.e. splittings proved to be a quite useful notion for investigations into the structure of the r.e. degrees. Important splitting theorems, like Sacks splitting [S1], Robinson splitting [R1] and Lachlan splitting [L3], use r.e. splittings.Since each r.e. splitting of a set induces a splitting of its degree, it is natural to study the relation between the degrees of (...) r.e. splittings and the degree splittings of a set. We say a setAhas thestrong universal splitting property if each splitting of its degree is represented by an r.e. splitting of itself, i.e., if for degA=b∪cthere is an r.e. splittingB, CofAsuch that degB=band degC=c. The goal of this paper is the study of this splitting property.In the literature some weaker splitting properties have been studied as well as splitting properties which imply failure of the SUSP. (shrink)

The Editors express their gratitude and appreciation to the indi-viduals listed below who served as referees for Informal Logic for Volumes 31 (2011) and 32 (2012).

I read Stefan Collini’s What are Universities For? last week with very mixed feelings. In the past, I’ve much admired his polemical essays on the REF, “impact”, the Browne Report, etc. in the London Review of Books and elsewhere: they speak to my heart. If you don’t know those essays, you can get some of their flavour from his latest article in the Guardian yesterday. But I found the book a disappointment. Perhaps the trouble is that Collini is too decent, (...) too high-minded, has too unrealistically exalted a view about what actually happens in universities which is too coloured by attitudes appropriate to the traditional humanities. And he is optimistic to the point of fantasy if he thinks that people are so susceptible to “the romance of ideas and the power of beauty” that they will want, or can be brought to want, lots and lots of universities in order to promote the ideas (as if they would suppose that the task of “conserving, understanding, extending and handing on to subsequent generations the intellectual, scientific, and artistic heritage of mankind” was clearly ill-served when there were only forty universities in England, as opposed to a hundred and whatever). (shrink)

The Joint International Conference on Logic Programming, sponsored by the Association for Logic Programming, is a major forum for presentations of research, applications, and implementations in this important area of computer science. Logic programming is one of the most promising steps toward declarative programming and forms the theoretical basis of the programming language Prolog and its various extensions. Logic programming is also fundamental to work in artificial intelligence, where it has been used for nonmonotonic and commonsense (...) reasoning, expert systems implementation, deductive databases, and applications such as computer-aided manufacturing. Krzysztof R. Apt is project leader at the Centre for Mathematics and Computer Science in Amsterdam and part-time Professor in Computer Science at the University of Amsterdam. Topics covered: Theory Foundations. Programming Languages. Implementation. Programming Methodologies and Tools. Applications. Deductive Databases. Artificial Intelligence. Parallelism. (shrink)

The First International Workshop brings together researchers from the theoretical ends of the logic programming and artificial intelligence communities to discuss their mutual interests. Logic programming deals with the use of models of mathematical logic as a way of programming computers, where theoretical AI deals with abstract issues in modeling and representing human knowledge and beliefs. One common ground is nonmonotonic reasoning, a family of logics that includes room for the kinds of variations that can be found (...) in human reasoning. Topics covered: Stable Semantics. Default Logic. AutoEpistemic Logic. Truth Maintenance Systems. Implementation Issues. Diagnosis. Applications. Inheritance Reasoning. Logics of Belief. Inconsistency and Non-Monotonicity. (shrink)

In their recent article “A Hierarchy of Classical and Paraconsistent Logics”, Eduardo Barrio, Federico Pailos and Damien Szmuc present novel and striking results about meta-inferential validity in various three valued logics. In the process, they have thrown open the door to a hitherto unrecognized domain of non-classical logics with surprising intrinsic properties, as well as subtle and interesting relations to various familiar logics, including classical logic. One such result is that, for each natural number n, there is a (...) class='Hi'>logic which agrees with classical logic on tautologies, inferences, meta-inferences, meta-meta-inferences, meta-meta-...-meta-inferences, but that disagrees with classical logic on n + 1-meta-inferences. They suggest that this shows that classical logic can only be characterized by defining its valid inferences at all orders. In this article, I invoke some simple symmetric generalizations of BPS’s results to show that the problem is worse than they suggest, since in fact there are logics that agree with classical logic on inferential validity to all orders but still intuitively differ from it. I then discuss the relevance of these results for truth theory and the classification problem. (shrink)

Game logics describe general games through powers of players for forcing outcomes. In particular, they encode an algebra of sequential game operations such as choice, dual and composition. Logic games are special games for specific purposes such as proof or semantical evaluation for first-order or modal languages. We show that the general algebra of game operations coincides with that over just logical evaluation games, whence the latter are quite general after all. The main tool in proving this is a (...) representation of arbitrary games as modal or first-order evaluation games. We probe how far our analysis extends to product operations on games. We also discuss some more general consequences of this new perspective for standard logic. (shrink)

This comprehensive text shows how various notions of logic can be viewed as notions of universal algebra providing more advanced concepts for those who have an introductory knowledge of algebraic logic, as well as those wishing to delve into more theoretical aspects.

The first full-length study of Robert Kilwardby's commentary on Aristotle's Prior Analytics, based on a study of the medieval manuscripts.