Online research in philosophy

This paper presents the progicnet programme. It proposes a general framework for probabilistic logic that can guide inference based on both logical and probabilistic input. After an introduction to the framework as such, it is illustrated by means of a toy example from psychometrics. It is shown that the framework can accommodate a number of approaches to probabilistic reasoning: Bayesian statistical inference, evidential probability, probabilistic argumentation, and objective Bayesianism. The framework thus provides insight into the relations between these approaches, it (...) illustrates how the results of different approaches can be combined, and it provides a basis for doing efficient inference in each of the approaches. (shrink)

In this paper we show the embedding of Hybrid Probabilistic Logic Programs into the rather general framework of Residuated Logic Programs, where the main results of (definite) logic programming are validly extrapolated, namely the extension of the immediate consequences operator of van Emden and Kowalski. The importance of this result is that for the first time a framework encompassing several quite distinct logic programming semantics is described, namely Generalized Annotated Logic Programs, Fuzzy Logic Programming, Hybrid Probabilistic Logic Programs, and Possibilistic (...) Logic Programming. Moreover, the embedding provides a more general semantical structure paving the way for defining paraconsistent probabilistic reasoning with a logic programming semantics. (shrink)

.  In this paper, adaptive logics are studied from the viewpoint of universal logic (in the sense of the study of common structures of logics). The common structure of a large set of adaptive logics is described. It is shown that this structure determines the proof theory as well as the semantics of the adaptive logics, and moreover that most properties of the logics can be proved by relying solely on the structure, viz. without invoking any specific properties of the logics (...) themselves. (shrink)

This paper develops connections between objective Bayesian epistemology—which holds that the strengths of an agent’s beliefs should be representable by probabilities, should be calibrated with evidence of empirical probability, and should otherwise be equivocal—and probabilistic logic. After introducing objective Bayesian epistemology over propositional languages, the formalism is extended to handle predicate languages. A rather general probabilistic logic is formulated and then given a natural semantics in terms of objective Bayesian epistemology. The machinery of objective Bayesian nets and objective credal nets (...) is introduced and this machinery is applied to provide a calculus for probabilistic logic that meshes with the objective Bayesian semantics. (shrink)

This volume arose out of an international, interdisciplinary academic network on Probabilistic Logic and Probabilistic Networks involving four of us (Haenni, Romeijn, Wheeler and Williamson), called Progicnet and funded by the Leverhulme Trust from 2006–8. Many of the papers in this volume were presented at an associated conference, the Third Workshop on Combining Probability and Logic (Progic 2007), held at the University of Kent on 5–7 September 2007. The papers in this volume concern either the special focus on the connection (...) between probabilistic logic and probabilistic networks or the more general question of the links between probability and logic. Here we introduce probabilistic logic, probabilistic networks, current and future directions of research and also the themes of the papers that follow. (shrink)

We introduce Kripke semantics for modal substructural logics, and provethe completeness theorems with respect to the semantics. Thecompleteness theorems are proved using an extended Ishihara's method ofcanonical model construction (Ishihara, 2000). The framework presentedcan deal with a broad range of modal substructural logics, including afragment of modal intuitionistic linear logic, and modal versions ofCorsi's logics, Visser's logic, Méndez's logics and relevant logics.

Current dynamic-epistemic logics model different types of information change in multi-agent scenarios. We generalize these logics to a probabilistic setting, obtaining a calculus for multi-agent update with three natural slots: prior probability on states, occurrence probabilities in the relevant process taking place, and observation probabilities of events. To match this update mechanism, we present a complete dynamic logic of information change with a probabilistic character. The completeness proof follows a compositional methodology that applies to a much larger class of dynamic-probabilistic (...) logics as well. Finally, we discuss how our basic update rule can be parameterized for different update policies, or learning methods. (shrink)

We consider two topological interpretations of the modal diamond—as the closure operator (C-semantics) and as the derived set operator (d-semantics). We call the logics arising from these interpretations C-logics and d-logics, respectively. We axiomatize a number of subclasses of the class of nodec spaces with respect to both semantics, and characterize exactly which of these classes are modally definable. It is demonstrated that the d-semantics is more expressive than the C-semantics. In particular, we show that the d-logics of the six (...) classes of spaces considered in the paper are pairwise distinct, while the C-logics of some of them coincide. (shrink)