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)

Logic Works is a critical and extensive introduction to logic. It asks questions about why systems of logic are as they are, how they relate to ordinary language and ordinary reasoning, and what alternatives there might be to classical logical doctrines. It considers how logical analysis can be applied to carefully represent the reasoning employed in academic and scientific work, better understand that reasoning, and identify its hidden premises. Aiming to be as much a reference work and (...) handbook for further, independent study as a course text, it covers more material than is typically covered in an introductory course. -/- Topics include: translation, proofs, and trees for sentential and predicate logic with identity, definite descriptions, and functional terms; normal forms; proofs and trees for the principal normal modal systems; an introduction to second order and quantified modal logic; formal syntax and semantics; mathematical induction; metatheory for many of these systems; semantics and trees for free logic, intuitionistic logic, and three-valued and paraconsistent logics. -/- A companion website contains a detailed student solutions manual with a running commentary on all starred exercises and a set of editable slides for instructors to customize their courses. (shrink)

How Logic Works is an introductory logic textbook that is different by design. Rather than teaching elementary symbolic logic as an abstract or rote mathematical exercise divorced from ordinary thinking, Hans Halvorson presents it as the skill of clear and rigorous reasoning, which is essential in all fields and walks of life, from the sciences to the humanities—anywhere that making good arguments, and spotting bad ones, is critical to success. Instead of teaching how to apply algorithms using “truth trees,” (...) as in the vast majority of logic textbooks, How Logic Works builds on and reinforces the innate human skills of making and evaluating arguments. It does this by introducing the methods of natural deduction, an approach that teaches students not only how to carry out a proof and solve a problem but also what the principles of valid reasoning are and how they can be applied to any subject. The book also allows students to transition smoothly to more advanced topics in logic by teaching them general techniques that apply to more complicated scenarios, such as how to formulate theories about specific subject matter. How Logic Works shows that formal logic—far from being only for mathematicians or a diversion from the really deep questions of philosophy and human life—is the best account we have of what it means to be rational. By teaching logic in a way that makes students aware of how they already use it, the book will help them to become even better thinkers. A concise, readable, and user-friendly introduction to elementary symbolic logic that primarily uses natural deduction rather than algorithmic “truth trees” Draws on more than two decades’ experience teaching introductory logic to undergraduates Provides a stepping stone to more advanced topics. (shrink)

One might poetically muse that computers have the essence both of logic and machines. Through the case of the history of Separation Logic, we explore how this assertion is more than idle poetry. Separation Logic works because it merges the software engineer’s conceptual model of a program’s manipulation of computer memory with the logical model that interprets what sentences in the logic are true, and because it has a proof theory which aids in the crucial problem of scaling (...) the reasoning task. Scalability is a central problem, and some would even say the central problem, in appli- cations of logic in computer science. Separation Logic is an interesting case because of its widespread success in verification tools. For these two senses of model—the engineering/conceptual and the logical—to merge in a genuine sense, each must maintain their norms of use from their home disciplines. When this occurs, both the logic and engineering benefit greatly. Seeking this intersection of two different senses of model provides a strategy for how computer scientists and logicians may be successful. Furthermore, the history of Separation Logic for analysing programs provides a novel case for philosophers of science of how software engineers and computer scientists develop models and the components of such models. We provide three contributions: an exploration of the extent of models merging that is necessary for success in computer science; an introduction to the technical details of Separation Logic, which can be used for reasoning about other exhaustible resources; and an introduction to the problems, process, and results of computer scientists for those outside the field. (shrink)

. This paper aims to highlight some peculiarities of the semiotic square, whose creation is due in particular to Greimas’ works. The starting point is the semiotic notion of complex term, which I regard as one of the main differences between Greimas’ square and Blanché’s hexagon. The remarks on the complex terms make room for a historical survey in Aristotle’s texts, where one can find the philosophical roots of the idea of middle term between two contraries and its relation (...) to notions such as difference, position and motion. In the Stagirite’s non-logical works, the theory of the intermediate, or middle term, represents an important link between opposition issues and ethics: this becomes a privileged perspective from which to reconsider the semiotic use of the square, i.e., its inclusion in the semio-narrative structures articulating the sense of texts. (shrink)

"In this essay, I wish to question the view that the distinction between medieval and early modern philosophy is primarily one of method. I shall argue that what has come to be known as the modern method in fact owes much to the natural philosophy of John Buridan (ca. 1295-1361), a secular arts master who taught at the University of Paris some three centuries before Descartes. Surrounded by conflicts over institutional governance and curricular disputes, Buridan emerged as a forceful voice (...) for the independence and autonomy of teachers in the faculty of arts, arguing that philosophy as properly practiced belonged to them, the "artists artistae", not to those who taught in the so-called 'higher' faculties of theology, law, and medicine. Now such voices had been heard before at Paris, most notably from Averroist arts masters in the late 13th and early 14th-centuries.(*) Buridan is different, however, because unlike Boethius of Dacia and John of Jandun, he knew how to make the case for artistic autonomy without denigrating the theology and thereby inviting official condemnation. His trick was not to argue that there are 'two truths', one acquired and the other revealed, which might well come into conflict with each other, or that propositions whose truth has been revealed in scripture in no way qualify as scientia. It was rather to recognize the profoundly different methods of theology and philosophy, without losing sight of the fact that what counts as evidence in a proof in natural philosophy does not work in a theological argument, even if both have the same conclusion, such as that the human soul is immortal. Buridan seems to think that if only people would respect the differences between the rules of philosophical and theological inquiry, no conflicts would arise. He is not so naive as to claim this could ever happen, of course. But it does explain why he almost always diagnoses such conflicts in terms of some logical or linguistic confusion on the part of the people who propose them. Buridan is also different because in him the secularizing sentiment already present in the Latin Averroists begins to take shape as a way of doing philosophy, i.e., as a philosophical grammar.. (shrink)

In this paper, I shed light on Kant’s notion of Erkenntnis or cognition by focusing on texts pertaining to Kant’s thoughts on logic. Although a passage from Kant’s Logik is widely referred to for understanding Kant’s conception of Erkenntnis, this work was not penned by Kant himself but rather compiled by Benjamin Jäsche. So, it is imperative to determine its fidelity to Kant’s thought. I compare the passage with other sources, including Reflexionen and students’ lecture notes. I argue that several (...) of the text’s peculiarities stem from Jäsche rather than Kant, but that nevertheless Jäsche largely got Kant's view right, with two major exceptions. First, Jäsche’s text fails to reproduce Kant’s key thesis that kennen and verstehen are jointly sufficient for Erkenntnis. Second, Jäsche’s text gives the false impression that Kant holds that animals have consciousness. (shrink)

Now we should have to answer the question: when were the questions on Perihermeneias written? Little is known about the chronology of Buridan's works. Even a relative date is difficult to establish. However, some remarks can be made. First, there is the fact that the questions on Perihermeneias are quoted several times in Tractatus I of the Summule (4), in a way that makes it highly probable that the Summule were written after the Questiones on Perihermeneias (5). Now, according (...) to professor Pinborg the first lectura of the Summule may be dated as early as the late 1320es (6), that is at the very beginning of Buridan's career as a teacher of philosophy at the university of Paris. This may be an indication for an early date of the Questiones on Perihermeneias, possibly as early as 1325. There are two other reasons for assuming that the commentary on Perihermeneias is one of Buridan's first works. The first clue is given by the places where Buridan refers to one of his own works: once he refers to his commentary on Porphyry's Isagoge (7), twice to his commentary on Aristotle's Metaphysics (8), and six times to his commentary on the Physics (9). The way in which he refers to these tracts seems also to be significant: the reference to his commentary on Porphyry's Isagoge shows that this work is of an earlier date than the present work. As to the other two works, he only refers to the number of the book in which he is going to treat a particular subject, not to the number of the question. A (cross)reference to the Summule is not given, although, as Pinborg remarks, there is a general doctrinal concordance between the two works. The questions on Metaphysics do not contain a (cross)-reference to the questions on Perihermeneias, at least not on the places where one would expect them. I am not certain about possible references occurring in the commentary on Physics. However, we should be very careful to draw conclusions from the occurrence of references, since it is always possible that we are dealing with a second or third lectura of the text.. (shrink)

I provide a survey of the contents of the works belonging to Aristotle's Organon in order to define their nature, in the light of his declared intentions and of other indications (mainly internal ones) about his purposes. No unifying conception of logic can be found in them, such as the traditional one, suggested by the very title Organon, of logic as a methodology of demonstration. Logic for him can also be formal logic (represented in the main by the De (...) Interpretatione), axiomatized syllogistic (represented in the main by the Prior Analytics) and a methodology of dialectical and rhetorical discussion. The consequent lack of unity presented by those works does not exclude that both the set of works called Analytics and the set of works concerning dialectic (Topics and Sophistici Elenchi) form a unity, and that a certain priority is attributed to the analytics with respect to dialectic. (shrink)

This is primarily a conceptual paper. The goal of the paper is to put into perspective the proof-theory of hybrid logic and in particular, try to give an answer to the following question: Why does the proof-theory of hybrid logic work so well compared to the proof-theory of ordinary modal logic?Roughly, there are two different kinds of proof systems for modal logic: Systems where the formulas involved in the rules are formulas of the object language, that is, ordinary modal-logical (...) formulas, and systems where the formulas involved in the rules are metalingustic formulas obtained by attaching labels representing possible worlds to ordinary modal-logical formulas. Systems of the second kind often also involve an explicit representation of the accessibility relation. From a proof-theoretic point of view, modal-logical systems of the first kind are less well-behaved than systems of the second kind.It turns out that this can be remedied by hybridization, that is, hybridization of modal logics enables the formulation of well-behaved proof systems without involving metalinguistic machinery. What has happened is that the metalinguistic machinery has been internalized in the object language. This gives an answer to the initial question, which is that the proof-theory of hybrid logic works so well because the metalinguistic semantic machinery has been internalized in the object language. (shrink)

The question discussed in this paper is the relation of the Topics to the two Analytics. The smaller works are here ignored.

The question discussed in this paper is the relation of the Topics to the two Analytics. The smaller works are here ignored.

In book 3 of On Abstinence from Animal Food, Porphyry is traditionally taken to argue that animals are rational and that it is, therefore, unjust to kill them for food. Since the vast majority of scholars endorse this interpretation, I call it ‘the consensus interpretation’. Yet, strangely enough, elsewhere in his corpus Porphyry claims that the non-human animals are irrational. Jonathan Barnes notices this discrepancy and suggests that an appeal to the distinction between specific and non-specific predication can resolve the (...) problem. This paper explains Barnes’ solution, but argues that it must ultimately be rejected. It concludes with a brief survey of other approaches to the problem, and with an outline of the proposed solution, in which the consensus interpretation of On Abstinence is rejected in favour of a dialectical reading of Book 3. Porphyry, this piece suggests, may not have believed that animals were rational after all. (shrink)

This book provides a historical and comparative study of logic in Arabic in Bosnia and Herzegovina, from the first texts, 16th century, to the end of the 19th ...

This paper surveys important work done in relevant logic in the past 10 years.

"Abelard composed four works on logic: (1) Introductiones Parvulorum, which consists of short glosses on Porphyry Eisagoge and Aristotle Categories and De Interpretatione; (2) Logica Ingredientibus (so called because ingredientibus is the first word of its text), which consists of longer glosses on the texts covered by the previous work together with Boethius' De Differentiis Topicis and was probably written while Abelard was teaching in Paris before 1120; (3) Logica Nostrorum Petitioni (so called because nostrorum petitioni are the first (...) words of its text), which consists of longer glosses on the Eisagoge and may date from the time of his teaching at the hermitage of the Paraclete; (4) Dialectica, which has the form of an independent work about the subjects covered by Boethius' logical writings and Victorinus' treatise De Definitionibus and seems to contain materials from different periods of Abelard's life but probably did not reach its final form until a late date, perhaps the time of his stay at Cluny shortly before his death. Of these the second and the fourth are the most valuable. The Dialectica indeed, though based, like that of Garland, chiefly on the works of Boethius and written with the prolixity which was all too common among medieval authors, is an original composition of great importance for the development of logic. Abelard's mind was the keenest (though not in all respects the most admirable) that had been devoted to the subject for more than a thousand years, and he approached his task with the belief that it was still possible to make discoveries: 'Non enim tanta fuit antiquorum scriptorum perfectio ut non et nostro doctrina indigeat studio, nec tantum in nobis mortalibus scientia potest crescere ut non ultra possit augmentum recipere.' (1) The Dialectica survives in a single manuscript which lacks the opening sections. Excerpts from it were published by Victor Cousin in 1836 in his Ouvrages inédits d' Abelard. But unfortunately the text was not printed in full until 1956, and before that date it was therefore not possible to appreciate the magnitude of Abelard's contribution to the doctrines we regard as characteristically medieval.. (shrink)

Pt. I. Writings on the theory of logic: I. Pure logic or the logic of quality apart from quantity. II. The substitution of similars. III. On the mechanical performance of logical inference. IV. On a general system of numerically definite reasoning.--Pt. II. John Stuart Mill's philosophy tested: I. On geometrical reasoning. II. On resemblance. III. The experimental methods. IV. Utilitarianism. V. On the method of difference.

Review by: Achim Blumensath The Bulletin of Symbolic Logic, Volume 19, Issue 3, Page 394-396, September 2013.

We examine the contrast between the “Newtonian style” and the Cartesian, hypothetico-deductive method in order to expand on George Smith's account of working hypotheses and theory-mediation. We stress the pivotal role of theory-mediation in turning experience into well-defined phenomena and introduce the complementary notions of conditional and independent evidence. Conditional evidence is evidence in favor of an hypothesis that is based on phenomena that would not be constituted as phenomena without the hypothesis in question. Direct evidence is evidence based on (...) phenomena that are independently available. We use the distinction to interrogate the role of mathematical representation as the most basic constitutive posit of the Newtonian style, as the working hypothesis that enables all further theory-mediation. Our primary examples are Newton's struggles with motion in fluids and his defense of the Laws of Motion. (shrink)