Arthur Prior and medieval logic

Though Arthur Prior is now best known for his founding of modern temporal logic and hybrid logic, much of his early philosophical career was devoted to history of logic and historical logic. This interest laid the foundations for both of his ground-breaking innovations in the 1950s and 1960s. Because of the important r?le played by Prior??s research in ancient and medieval logic in his development of temporal and hybrid logic, any student of Prior, temporal logic, or hybrid logic should be familiar with the medieval logicians and their work. In this article we give an overview of Prior??s work in ancient and medieval logic.     

Hybrid Probabilistic Logic Programs as Residuated Logic Programs

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.     

Using Hybrid Logic for Coping with Functions in Subset Spaces

We extend Moss and Parikh’s modal logic for subset spaces by adding, among other things, state-valued and set-valued functions. This is done with the aid of some basic concepts from hybrid logic. We prove the soundness and completeness of the derived logics with regard to the class of all correspondingly enriched subset spaces, and show that these logics are decidable.     

The expressibility of fragments of Hybrid Graph Logic on finite digraphs

Hybrid Graph Logic is a logic designed for reasoning about graphs and is built from a basic modal logic, augmented with the use of nominals and a facility to verify the existence of paths in graphs. We study the finite model theory of Hybrid Graph Logic. In particular, we develop pebble games for Hybrid Graph Logic and use these games to exhibit strict infinite hierarchies involving fragments of Hybrid Graph Logic when the logic is used to define problems involving finite digraphs. These fragments are parameterized by the quantifier-rank of formulae along with the numbers of propositional symbols and nominals that are available. We ascertain exactly the relative definability of these parameterized fragments of the logic.     

Logic,Logic, and Logic

In his recent paper in History and Philosophy of Logic, John Kearns argues for a solution of the Liar paradox using an illocutionary logic (Kearns 2007 Kearns, J. 2007. ‘An illocutionary logical explanation of the Liar Paradox’. History and Philosophy of Logic, 28: 31–66. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). Paraconsistent approaches, especially dialetheism, which accepts the Liar as being both true and false, are rejected by Kearns as making no ‘clear sense’ (p. 51). In this critical note, I want to highlight some shortcomings of Kearns' approach that concern a general difficulty for supposed solutions to (semantic) antinomies like the Liar. It is not controversial that there are languages which avoid the Liar. For example, the language which consists of the single sentence ‘Benedict XVI was born in Germany’ lacks the resources to talk about semantics at all and thus avoids the Liar. Similarly, more interesting languages such as the propositional calculus avoid the Liar by lacking the power to express semantic concepts or to quantify over propositions. Kearns also agrees with the dialetheist claim that natural languages are semantically closed (i.e. are able to talk about their sentences and the semantic concepts and distinctions they employ). Without semantic closure, the Liar would be no real problem for us (speakers of natural languages). But given the claim, the expressive power of natural languages may lead to the semantic antinomies. The dialetheist argues for his position by proposing a general hypothesis (cf. Bremer 2005 Bremer, M. 2005. An Introduction to Paraconsistent Logics, Bern: Lang.  [Google Scholar], pp. 27–28): ‘(Dilemma) A linguistic framework that solves some antinomies and is able to express its linguistic resources is confronted with strengthened versions of the antinomies’. Thus, the dialetheist claims that either some semantic concepts used in a supposed solution to a semantic antinomy are inexpressible in the framework used (and so, in view of the claim, violate the aim of being a model of natural language), or else old antinomies are exchanged for new ones. One horn of the dilemma is having inexpressible semantic properties. The other is having strengthened versions of the antinomies, once all semantic properties used are expressible. This dilemma applies, I claim, to Kearns' approach as well.     

Arthur Peacocke

Drawing on animal ethological studies, this article considers the possibility of a form of morality existing in animals and its relationship with human morality. Given this capacity, I argue that first we need to reflect more carefully on human sin and evil in evolutionary terms. Second, I question the adequacy of the traditional divide between “moral” and “natural” evil as well as consider the possibility of anthropogenic evil. Third, I suggest that a theological response to nonhuman morality should include discussion of the atonement, but traditional categories prove inadequate. Fourth, drawing on Sergii Bulgakov, I explore the idea of shadow sophia as representing a multivocal theodicy that is capable of holding together a tapestry of different theological responses to evil. Finally, I discuss the redemption of nature in the light of the foregoing discussion.     

Arthur Schopenhauer and Andras Angyal

Schopenhauer attributed will to both humans and objects, and commentators have dismissed the notion that objects have will. It is proposed that by focusing on our perception of the environment, rather than the environment itself, the theory of personality proposed by Angyal provides a way of attributing forces to both the individual and to the environment.     

Prior knowledge and recognition

The purpose of this series of experiments was to determine if and when word recognition would depend on the number of related concepts represented in permanent memory. Words defining either large or small rhyme or meaning categories were studied and tested under various conditions. The results indicated that rhyme category size influenced recognition whenever rhyme was emphasized during both study and testing phases. Words belonging to larger rhyme sets were not recognized as well as those belonging to smaller rhyme sets. In contrast, meaning-related set size had no effect on recognition. These and other findings indicate that the breadth of prior knowledge can influence recognition but only under limited conditions that reactivate this knowledge at test.     

Prior probabilities

The theoretical construction and practical use of prior probabilities, in particular for systems having many degrees of freedom, are investigated. It becomes clear that it is operationally unsound to use mutually consistent priors if one wishes to draw sensible conclusions from practical experiments. The prior cannot usefully be identified with a state of knowledge, and indeed it is not so identified in common scientific practice. Rather, it can be identified with the question one asks. Accordingly, priors are free constructions. Their informal, ill-defined and subjective characteristics must carry over into the conclusions one chooses to draw from experiments or observations.     

On Argumentation Logic and Propositional Logic

This paper studies the relationship between Argumentation Logic (AL), a recently defined logic based on the study of argumentation in AI, and classical Propositional Logic (PL). In particular, it shows that AL and PL are logically equivalent in that they have the same entailment relation from any given classically consistent theory. This equivalence follows from a correspondence between the non-acceptability of (arguments for) sentences in AL and Natural Deduction (ND) proofs of the complement of these sentences. The proof of this equivalence uses a restricted form of ND proofs, where hypotheses in the application of the Reductio of Absurdum inference rule are required to be “relevant” to the absurdity derived in the rule. The paper also discusses how the argumentative re-interpretation of PL could help control the application of ex-falso quodlibet in the presence of inconsistencies.     

Prior experience and complex procedures

The role of prior knowledge in learning complex procedures was investigated in a transfer task in which subjects learned two related procedures in sequence. In Experiment 1, we manipulated the conceptual and structural similarity between the two procedures; in Experiment 2, we manipulated whether the order of the steps within subprocedures was the same or different during training and transfer, or whether the order of the subprocedures was the same or different. The results lead us to hypothesize that transfer in complex procedures is mediated primarily by a memory for specific steps rather than by conceptual understanding or problem solving. In particular, we were able to model the results precisely on the assumption that subjects use superficial similarity to retrieve the sequences of steps needed to perform segments of the procedure.     

Prior knowledge and exemplar frequency

New concepts can be learned by statistical associations, as well as by relevant existing knowledge. We examined the interaction of these two processes by manipulating exemplar frequency and thematic knowledge and considering their interaction through computational modeling. Exemplar frequency affects category learning, with high-frequency items learned more quickly than low-frequency items, and prior knowledge usually speeds category learning. In two experiments in which both of these factors were manipulated, we found that the effects of frequency are greatly reduced when stimulus features are linked by thematic prior knowledge and that frequency effects on single stimulus features can actually be reversed by knowledge. We account for these results with the knowledge resonance model of category learning (Rehder & Murphy, 2003) and conclude that prior knowledge may change representations so that empirical effects, such as those caused by frequency manipulations, are modulated.