ONE TRUE LOGIC?

This is a paper about the constituents of arguments. It argues that several different kinds of truth-bearer may be taken to compose arguments, but that none of the obvious candidates—sentences, propositions, sentence/truth-value pairs etc.—make sense of logic as it is actually practiced. The paper goes on to argue that by answering the question in different ways, we can generate different logics, thus ensuring a kind of logical pluralism that is different from that of J. C. Beall and Greg Restall.     

Pandora: A Reasoning Toolbox using Natural Deduction Style

Pandora is a tool for supporting the learning of first ordernatural deduction. It includes a help window, an interactivecontext sensitive tutorial known as the "e-tutor" and facilitiesto save, reload and export to LATEX. Every attempt to applya natural deduction rule is met with either success or a helpfulerror message, providing the student with instant feedback.Detailed electronic logs of student usage are recorded for evaluationpurposes. This paper describes the basic functionality, thee-tutor, our experiences of using the tool in teaching and ourfuture plans.     

How fish do geometry in large and in small spaces

It has been shown that children and non-human animals seem to integrate geometric and featural information to different extents in order to reorient themselves in environments of different spatial scales. We trained fish (redtail splitfins, Xenotoca eiseni) to reorient to find a corner in a rectangular tank with a distinctive featural cue (a blue wall). Then we tested fish after displacement of the feature on another adjacent wall. In the large enclosure, fish chose the two corners with the feature, and also tended to choose among them the one that maintained the correct arrangement of the featural cue with respect to geometric sense (i.e. left-right position). In contrast, in the small enclosure, fish chose both the two corners with the features and the corner, without any feature, that maintained the correct metric arrangement of the walls with respect to geometric sense. Possible reasons for species differences in the use of geometric and non-geometric information are discussed.     

Abductive reasoning in neural-symbolic systems

Abduction is or subsumes a process of inference. It entertains possible hypotheses and it chooses hypotheses for further scrutiny. There is a large literature on various aspects of non-symbolic, subconscious abduction. There is also a very active research community working on the symbolic (logical) characterisation of abduction, which typically treats it as a form of hypothetico-deductive reasoning. In this paper we start to bridge the gap between the symbolic and sub-symbolic approaches to abduction. We are interested in benefiting from developments made by each community. In particular, we are interested in the ability of non-symbolic systems (neural networks) to learn from experience using efficient algorithms and to perform massively parallel computations of alternative abductive explanations. At the same time, we would like to benefit from the rigour and semantic clarity of symbolic logic. We present two approaches to dealing with abduction in neural networks. One of them uses Connectionist Modal Logic and a translation of Horn clauses into modal clauses to come up with a neural network ensemble that computes abductive explanations in a top-down fashion. The other combines neural-symbolic systems and abductive logic programming and proposes a neural architecture which performs a more systematic, bottom-up computation of alternative abductive explanations. Both approaches employ standard neural network architectures which are already known to be highly effective in practical learning applications. Differently from previous work in the area, our aim is to promote the integration of reasoning and learning in a way that the neural network provides the machinery for cognitive computation, inductive learning and hypothetical reasoning, while logic provides the rigour and explanation capability to the systems, facilitating the interaction with the outside world. Although it is left as future work to determine whether the structure of one of the proposed approaches is more amenable to learning than the other, we hope to have contributed to the development of the area by approaching it from the perspective of symbolic and sub-symbolic integration.

《易经》:人类科学思维和审美思维方式的精典阐释

一本诞生于五千年前的中国古书《易经》,已经包含着深刻的现代科学数理逻辑原理,且与美学的审美逻辑原理互为支持、互为表里,使这两大类本来被认为水火不相容的领域及其独具的思维方式得到了高度完善统一的阐释。从这样的角度来看《易经》,也许会有助于目前心理学界对思维方式及逻辑问题的研究,拓开一条崭新的思路。     

Combining Possibilities and Negations

Combining non-classical (or sub-classical) logics is not easy, but it is very interesting. In this paper, we combine nonclassical logics of negation and possibility (in the presence of conjunction and disjunction), and then we combine the resulting systems with intuitionistic logic. We will find that Kracht's results on the undecidability of classical modal logics generalise to a non-classical setting. We will also see conditions under which intuitionistic logic can be combined with a non-intuitionistic negation without corrupting the intuitionistic fragment of the logic.     

On Different Intuitionistic Calculi and Embeddings from Int to S4

In this paper, we compare several cut-free sequent systems for propositional intuitionistic logic Intwith respect to polynomial simulations. Such calculi can be divided into two classes, namely single-succedent calculi (like Gentzen's LJ) and multi-succedent calculi. We show that the latter allow for more compact proofs than the former. Moreover, for some classes of formulae, the same is true if proofs in single-succedent calculi are directed acyclic graphs (dags) instead of trees. Additionally, we investigate the effect of weakening rules on the structure and length of dag proofs.The second topic of this paper is the effect of different embeddings from Int to S4. We select two different embeddings from the literature and show that translated (propositional) intuitionistic formulae have sometimes exponentially shorter minimal proofs in a cut-free Gentzen system for S4than the original formula in a cut-free single-succedent Gentzen system for Int. Moreover, the length and the structure of proofs of translated formulae crucially depend on the chosen embedding.     

On the Nature of Continuous Physical Quantities in Classical and Quantum Mechanics

Journal of Philosophical Logic - Within the traditional Hilbert space formalism of quantum mechanics, it is not possible to describe a particle as possessing, simultaneously, a sharp position value...