Journal of Applied Logic最新文献

In [39], Imre Lakatos influentially argued that Carnapian inductive logic was a degenerate research programme. This paper argues that Lakatos's criticism was mistaken and that, according to Lakatos's own standards, Carnapian inductive logic was progressive rather than degenerate.

This editorial explains the scope of the special issue and provides a thematic introduction to the contributed papers.

Within the framework of (Unary) Pure Inductive Logic we investigate four possible formulations of a probabilistic principle of analogy based on a template considered by Paul Bartha in the Stanford Encyclopedia of Philosophy [1] and give some characterizations of the probability functions which satisfy them. In addition we investigate an alternative interpretation of analogical support, also considered by Bartha, based not on the enhancement of probability but on the creation of possibility.

We describe an integrated approach to vagueness and uncertainty within a propositional logic setting and based on a combination of three valued logic and probability. Three valued valuations are employed in order to model explicitly borderline cases and in this context we give an axiomatic characterisation of two well known three valued models; supervaluations and Kleene valuations. We then demonstrate the close relationship between Kleene valuations and a sub-class of supervaluations. Belief pairs are lower and upper measures on the sentences of the language generated from a probability distribution defined over a finite set of three valued valuations. We describe links between these measures and other uncertainty theories and we show the close relationship between Kleene belief pairs and a sub-class of supervaluation belief pairs. Finally, a probabilistic approach to conditioning is explored within this framework.

Ordinary quantum logic has well known pathologies rendering it useless for the purposes of computation. However, loosely related logics, based upon variants of Girard's Linear Logic, have been found useful in the context of quantum computation. In one sense, the use of such computational schemes affords a meta level view of the possible provenance of certain expressions not otherwise apparent. Since such logics are presumed to encapsulate the essential behavior of quantum “resources” we may entertain the question as to whether this logical or computational approach could have any bearing upon quantum physics itself. In this article we address the question of the genesis of certain fundamental Lagrangians, namely those occurring in the standard model. If a certain set of sentences in a logic are added to the set of axioms of the logic the resulting structure is generally called a theory by logicians. In this paper we shall introduce a version of such a logic and deduce some of its physical ramifications. Namely, we will show that there is a single type of sequent that, when added to the logical calculus at hand as an axiom, generates in the theory so defined, series whose leading terms match exactly the Yang–Mills Lagrangian density (including a gauge fixing term) and also the Einstein–Hilbert Lagrangian density, most of the remaining terms being negligible at low intensities in both cases. By expanding the logic somewhat, in the manner of second quantization, we are able also to give an account of interaction terms in the Yang–Mills case. This shows that there is a common form ancestral to all the Lagrangians of the standard model in the ensemble of “evolutionary” trees provided by deductions in a certain clearly specified logic, and reveals the differences between the Yang–Mills and gravitational kinetic terms. Thus we acquire a new paradigm for “unification” of the fundamental forces at the level of the underlying logic.

We study the computational complexity of bribery and manipulation schemes for sports tournaments with uncertain information. We introduce a general probabilistic model for multi-round tournaments and consider several special types of tournament: challenge (or caterpillar); cup; and round robin. In some ways, tournaments are similar to the sequential pair-wise, cup and Copeland voting rules. The complexity of bribery and manipulation are well studied for elections, usually assuming deterministic information about votes and results. We assume that for tournament entrants i and j, the probability that i beats j and the costs of lowering each probability by fixed increments are known to the manipulators. We provide complexity analyses for several problems related to manipulation and bribery for the various types of tournaments. Complexities range from probabilistic log space to ${\mathrm{NP}}^{\mathrm{PP}}$. This shows that the introduction of uncertainty into the reasoning process drastically increases the complexity of bribery problems in some instances.

OCF-networks provide the possibility to combine qualitative information expressed by rankings of (conditional) formulas with the strong structural information of a network, in this respect being a qualitative variant of the better known Bayesian networks. Like for Bayesian networks, a global ranking function can be calculated quickly and efficiently from the locally distributed information, whereas the latter significantly reduces the exponentially high complexity of the semantical ranking approach. This qualifies OCF-networks for applications. However, in practical applications the provided ranking information may not be in the format needed to be represented by an OCF-network, or some values may be simply missing. In this paper, we present techniques for filling in the missing values using methods of inductive reasoning and we elaborate on formal properties of OCF-networks.

A Dempster–Shafer theory based model of assertion is proposed for multi-agent communications so as to capture both epistemic and strategic uncertainty. Treating assertion as a choice problem, we argue that for complex multi-agent communication systems, individual agents will only tend to have sufficient information to allow them to formulate imprecise strategies for choosing between different possible true assertions. In a propositional logic setting, an imprecise assertion strategy is defined as a functional mapping between a valuation and a set of true sentences, where the latter is assumed to contain the optimal assertion given that particular state of the world. Uncertainty is then quantified in terms of probability distributions defined on the joint space of valuations and strategies, naturally leading to Dempster–Shafer belief and plausibility measures on sets of possible assertions. This model is extended so as to include imprecise valuations and to provide a meta-level treatment of weak and strong assertions. As a case study, we consider the application of our proposed assertion models to the problem of choosing between a number of different vague descriptions, in the context of both epistemic and supervaluationist approaches to vagueness.

This work introduces the Attack–Support Argumentation Framework (ASAF), an approach to abstract argumentation that allows for the representation and combination of attack and support relations. This framework extends the Argumen-tation Framework with Recursive Attacks (AFRA) in two ways. Firstly, it adds a support relation enabling to express support for arguments; this support can also be given to attacks, and to the support relation itself. Secondly, it extends AFRA's attack relation by allowing attacks to the aforementioned support relation. Moreover, since the support relation of the ASAF has a necessity interpretation, the ASAF also extends the Argumentation Framework with Necessities (AFN). Thus, the ASAF provides a unified framework for representing attack and support for arguments, as well as attack and support for the attack and support relations at any level.