A Sound and Complete Tableau Calculus for Reasoning about only Knowing and Knowing at Most

We define a tableau calculus for the logic of only knowing and knowing at most ON, which is an extension of Levesque's logic of only knowing O. The method is based on the possible-world semantics of the logic ON, and can be considered as an extension of known tableau calculi for modal logic K45. From the technical viewpoint, the main features of such an extension are the explicit representation of "unreachable" worlds in the tableau, and an additional branch closure condition implementing the property that each world must be either reachable or unreachable. The calculus allows for establishing the computational complexity of reasoning about only knowing and knowing at most. Moreover, we prove that the method matches the worst-case complexity lower bound of the satisfiability problem for both ON and O. With respect to [22], in which the tableau calculus was originally presented, in this paper we both provide a formal proof of soundness and completeness of the calculus, and prove the complexity results for the logic ON.     

Graph‐Theoretic Properties of Networks Based on Word Association Norms: Implications for Models of Lexical Semantic Memory

We compared the ability of three different contextual models of lexical semantic memory (BEAGLE, Latent Semantic Analysis, and the Topic model) and of a simple associative model (POC) to predict the properties of semantic networks derived from word association norms. None of the semantic models were able to accurately predict all of the network properties. All three contextual models over‐predicted clustering in the norms, whereas the associative model under‐predicted clustering. Only a hybrid model that assumed that some of the responses were based on a contextual model and others on an associative network (POC) successfully predicted all of the network properties and predicted a word's top five associates as well as or better than the better of the two constituent models. The results suggest that participants switch between a contextual representation and an associative network when generating free associations. We discuss the role that each of these representations may play in lexical semantic memory. Concordant with recent multicomponent theories of semantic memory, the associative network may encode coordinate relations between concepts (e.g., the relation between pea and bean, or between sparrow and robin), and contextual representations may be used to process information about more abstract concepts.     

Tableau reductions: Towards an optimal decision procedure for the modal necessity

We present a new prefixed tableau system $\mathsf{TK}$ for verification of validity in modal logic $\mathsf{K}$. The system $\mathsf{TK}$ is deterministic, it uniquely generates exactly one proof tree for each clausal representation of formulas, and, moreover, it uses some syntactic reductions of prefixes. $\mathsf{TK}$ is defined in the original methodology of tableau systems, without any external technique such as backtracking, backjumping, etc. Since all the necessary bookkeeping is built into the rules, the system is not only a basis for a validity algorithm, but is itself a decision procedure. We present also a deterministic tableau decision procedure which is an extension of $\mathsf{TK}$ and can be used for the global assumptions problem.     

Constraints for Input/Output Logics

In a previous paper we developed a general theory of input/output logics. These are operations resembling inference, but where inputs need not be included among outputs, and outputs need not be reusable as inputs. In the present paper we study what happens when they are constrained to render output consistent with input. This is of interest for deontic logic, where it provides a manner of handling contrary-to-duty obligations. Our procedure is to constrain the set of generators of the input/output system, considering only the maximal subsets that do not yield output conflicting with a given input. When inputs are authorised to reappear as outputs, both maxichoice revision in the sense of Alchourrón/Makinson and the default logic of Poole emerge as special cases, and there is a close relation with Reiter default logic. However, our focus is on the general case where inputs need not be outputs. We show in what contexts the consistency of input with output may be reduced to its consistency with a truth-functional combination of components of generators, and under what conditions constrained output may be obtained by a derivation that is constrained at every step.     

A Calculus of Substitutions for DPL

We consider substitutions in order sensitive situations, having in the back of our minds the case of dynamic predicate logic (DPL) with a stack semantics. We start from the semantic intuition that substitutions are move instructions on stacks: the syntactic operation [y/x] is matched by the instruction to move the value of the y-stack to the x-stack. We can describe these actions in the positive fragment of DPLE. Hence this fragment counts as a logic for DPL-substitutions. We give a calculus for the fragment and prove soundness and completeness.     

A Duality for the Algebras of a Łukasiewicz <Emphasis Type="Italic">n</Emphasis> + 1-valued Modal System

In this paper, we develop a duality for the varieties of a Łukasiewicz n + 1-valued modal system. This duality is an extension of Stone duality for modal algebras. Some logical consequences (such as completeness results, correspondence theory...) are then derived and we propose some ideas for future research. Presented by Daniele Mundici     

Conditionals and consequences

We examine the notion of conditionals and the role of conditionals in inductive logics and arguments. We identify three mistakes commonly made in the study of, or motivation for, non-classical logics. A nonmonotonic consequence relation based on evidential probability is formulated. With respect to this acceptance relation some rules of inference of System P are unsound, and we propose refinements that hold in our framework.     

The effect of development and individual differences in pointing comprehension of dogs

In spite of the rather different procedures actually used in comparative studies to test the ability of different species to rely on the human pointing gesture, there is no debate on the high performance of dogs in such tasks. Very little is known, however, on the course through which they acquire this ability or the probable factors influencing the process. Important developmental questions have remained unsolved and also some methodological concerns should be addressed before we can convincingly argue for one interpretation or another. In this study we tested 180 dogs of different age (from 2 months to adults) to investigate their performance in the human distal momentary pointing gesture. The results, analyzed at both the group and the individual levels, showed no difference in the performance according to age, indicating that in dogs the comprehension of the human pointing may require only very limited and rapid early learning to fully develop. Interestingly, neither the keeping conditions nor the time spent in active interaction with the owner, and not even some special (agility) training for using human visual cues, had significant effect on the success and explained individual differences. The performance of the dogs was rather stable over time: during the 20 trials within a session and even when subsamples of different age were repeatedly tested. Considering that in spite of the general success at the group level, more than half of the dogs were not successful at the individual level, we revealed alternative “decision-making rules” other than following the pointing gesture of the experimenter. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.

Giles’s Game and the Proof Theory of Łukasiewicz Logic

In the 1970s, Robin Giles introduced a game combining Lorenzen-style dialogue rules with a simple scheme for betting on the truth of atomic statements, and showed that the existence of winning strategies for the game corresponds to the validity of formulas in Łukasiewicz logic. In this paper, it is shown that ‘disjunctive strategies’ for Giles’s game, combining ordinary strategies for all instances of the game played on the same formula, may be interpreted as derivations in a corresponding proof system. In particular, such strategies mirror derivations in a hypersequent calculus developed in recent work on the proof theory of Łukasiewicz logic. Presented by Daniele Mundici     

The Tense Logic for Master Argument in Prior’s Reconstruction

In this paper we examine Prior’s reconstruction of Master Argument [4] in some modal-tense logic. This logic consists of a purely tense part and Diodorean definitions of modal alethic operators. Next we study this tense logic in the pure tense language. It is the logic K _t 4 plus a new axiom (P): ‘p Λ G p ⊃ P G p’. This formula was used by Prior in his original analysis of Master Argument. (P) is usually added as an extra axiom to an axiomatization of the logic of linear time. In that case the set of moments is a total order and must be left-discrete without the least moment. However, the logic of Master Argument does not require linear time. We show what properties of the set of moments are exactly forced by (P) in the reconstruction of Prior. We make also some philosophical remarks on the analyzed reconstruction. Presented by Jacek Malinowski