Probability and logic

The paper is an attempt to show that the formalism of subjective probability has a logical interpretation of the sort proposed by Frank Ramsey: as a complete set of constraints for consistent distributions of partial belief. Though Ramsey proposed this view, he did not actually establish it in a way that showed an authentically logical character for the probability axioms (he started the current fashion for generating probabilities from suitably constrained preferences over uncertain options). Other people have also sought to provide the probability calculus with a logical character, though also unsuccessfully. The present paper gives a completeness and soundness theorem supporting a logical interpretation: the syntax is the probability axioms, and the semantics is that of fairness (for bets).     

Proof Nets for the Multimodal Lambek Calculus

We present a novel way of using proof nets for the multimodal Lambek calculus, which provides a general treatment of both the unary and binary connectives. We also introduce a correctness criterion which is valid for a large class of structural rules and prove basic soundness, completeness and cut elimination results. Finally, we will present a correctness criterion for the original Lambek calculus Las an instance of our general correctness criterion.     

A logic of intention and attempt

We present a modal logic called (logic of intention and attempt) in which we can reason about intention dynamics and intentional action execution. By exploiting the expressive power of , we provide a formal analysis of the relation between intention and action and highlight the pivotal role of attempt in action execution. Besides, we deal with the problems of instrumental reasoning and intention persistence.     

Logic with numbers

Many people regard utility theory as the only rigorous foundation for subjective probability, and even de Finetti thought the betting approach supplemented by Dutch Book arguments only good as an approximation to a utility-theoretic account. I think that there are good reasons to doubt this judgment, and I propose an alternative, in which the probability axioms are consistency constraints on distributions of fair betting quotients. The idea itself is hardly new: it is in de Finetti and also Ramsey. What is new is that it is shown that probabilistic consistency and consequence can be defined in a way formally analogous to the way these notions are defined in deductive (propositional) logic. The result is a free-standing logic which does not pretend to be a theory of rationality and is therefore immune to, among other charges, that of “logical omniscience”.     

Termination of logic programs with imperfect information: applications and query procedure

A general logic programming framework allowing for the combination of several adjoint lattices of truth-values is presented. The language is sorted, enabling the combination of several reasoning forms in the same knowledge base. The contribution of the paper is two-fold: on the one hand, sufficient conditions guaranteeing termination of all queries for the fix-point semantics for a wide class of sorted multi-adjoint logic programs are presented and related to some well-known probability-based formalisms; in addition, we specify a general non-deterministic tabulation goal-oriented query procedure for sorted multi-adjoint logic programs over complete lattices. We prove its soundness and completeness as well as independence of the selection ordering. We apply the termination results to probabilistic and fuzzy logic programming languages, enabling the use of the tabulation proof procedure for query answering.     

The use of artificial neural networks and multiple linear regression in modelling work–health relationships: Translating theory into analytical practice

Although psychological theory acknowledges the existence of complex systems and the importance of nonlinear effects, linear statistical models have been traditionally used to examine relationships between environmental stimuli and outcomes. The way we analyse these relationships does not seem to reflect the way we conceptualize them. The present study investigated the application of connectionism (artificial neural networks) to modelling the relationships between work characteristics and employee health by comparing it with a more conventional statistical linear approach (multiple linear regression) on a sample of 1003 individuals in employment. Comparisons of performance metrics indicated differences in model fit, with neural networks to some extent outperforming the linear regression models, such that R ² for worn-out and job satisfaction were significantly higher in the neural networks. Most importantly, comparisons revealed that the predictors in the two approaches differed in their relative importance for predicting outcomes. The improvement is attributed to the ability of the neural networks to model complex nonlinear relationships. Being unconstrained by assumptions of linearity, they can provide a better approximation of such psychosocial phenomena. Nonlinear approaches are often better fitted for purpose, as they conform to the need for correspondence between theory, method, and data.     

The give-or-take-some dilemma: An empirical investigation of a hybrid social dilemma

We describe and empirically investigate a hybrid social dilemma that merges give-some and take-some dilemmas by allowing individuals to choose to either give or to take resources from a shared resource pool. Study 1 finds that (a) group size increases the inequality among group members and the likelihood of creating the public good, while reducing the amount of wasted resources; (b) larger bonuses increase provision rates; and (c) asymmetry in the wealth distribution of the group members induces higher levels of inequality of the final outcomes. Following the logic of appropriateness, players with high (low) endowments were more likely to give toward (take from) the shared resource. Study 2 finds that the tendency of the players with high (low) endowments to give (take) is amplified as the difference between endowment levels increased, and the players’ behavior is correlated with, and predictable from, independent judgments of what is perceived as appropriate.     

The Hennessy–Milner equivalence for continuous time stochastic logic with mu-operator

A continuous stochastic logic with a μ-operator μCSL is defined, and an interpretation through stochastic relations is proposed. We investigate morphisms for models of μCSL, showing that the associated congruences can be used for an investigation of bisimilarity. The Hennessy–Milner equivalence for μCSL is discussed, and it is shown that models are equivalent iff they are bisimilar, using a general criterion for bisimilarity from the theory of stochastic relations.