Perceived optimality of competing solutions to the Euclidean travelling salesperson problem

The Travelling Salesperson Problem (TSP) is a nondeterministic-polynomial hard (NP-hard) combinatorial problem that occurs in a wide range of industrial domains, including logistics, route finding, and computer wiring. Interestingly, despite the problem’s inherent computational difficulty, when presented in Euclidean space (ETSP), human participants can produce close-to-optimal solutions in near-linear time. However, when asked to compare and select the most optimum solution from a set of pre-defined competing solution options, participants can struggle. In this study we investigate this paradox by asking participants to compare four closed-loop Euclidean TSP solutions, in order to determine which solution they perceived to have the most optimal tour cost. We hypothesise that the extracted geometric properties have an effect on stimulus selection in a discrimination task (selection or no selection). Accordingly, we extracted four geometric properties from competing stimuli in order to create a perceptual activation function. Predictive analytics demonstrated that a classification model could identify the most optimal solution 97% of the time using the perceptual activation scores alone, yet human participants only correctly determined the most optimal solution 47% of the time. Mixed-effects models suggest that ‘likelihood of stimulus selection’ can be modelled as a function of the weighted coefficients of competing perceptual activation scores within each trial; however only a small amount of the variance is explained by these perceptual activation scores. Finally, a drift–diffusion model was used to create a theoretical framework of how likelihood of stimulus selection is influenced by competing perceptual activators. Our study highlights a novel way of extracting and analysing the importance of geometric properties that influence ETSP discrimination tasks, and links this analysis to human behaviour when discriminating between competing ETSP solutions.     

Expansion and Contraction of Finite States

We present a theory that copes with the dynamics of inconsistent information. A method is set forth to represent possibly inconsistent information by a finite state. Next, finite operations for expansion and contraction of finite states are given. No extra-logical element — a choice function or an ordering over (sets of) sentences — is presupposed in the definition of contraction. Moreover, expansion and contraction are each other's duals. AGM-style characterizations of these operations follow.     

A Modal Sortal Logic

An intensional semantic system for languages containing, in their logical syntax, sortal quantifiers, sortal identities, (second-order) quantifiers over sortals and the necessity operator is constructed. This semantics provides non-standard assignments to predicate expressions, which diverge in kind from the entities assigned to sortal terms by the same semantic system. The nature of the entities assigned to predicate expressions shows, at the same time, that there is an internal semantic connection between those expressions and sortal terms. A formal logical system is formulated that is proved to be absolutely consistent, sound and complete with respect to the intensional semantic system.     

Separating the wheat from the chaff: does discriminating between diagnostic and nondiagnostic information eliminate the dilution effect?

The dilution effect refers to the finding that judgments are often unduly influenced by nondiagnostic information, producing regressive judgment. Because the dilution effect is a problem in various domains, strategies to control the impact of nondiagnostic information were explored by drawing on a perceptual and a conversational account of the dilution effect. Three experiments (n = 259) demonstrate that explicit instructions to discriminate between diagnostic and nondiagnostic information did not reduce the dilution effect. Rather, consistent with a perceptual explanation but not consistent with a conversational explanation, the dilution effect disappeared only when participants engage in perceptual control, that is, when they actively remove nondiagnostic pieces of information before making a judgment. Copyright © 2004 John Wiley & Sons, Ltd.     

A family of Gödel hybrid logics

In this paper, we define a family of fuzzy hybrid logics that are based on Gödel logic. It is composed of two infinite-valued versions called ${\mathsf{GH}}_{\infty }$ and ${\mathsf{WGH}}_{\infty }$, and a sequence of finitary valued versions ${({\mathsf{GH}}_n)}_{0<n<\infty }$. We define decision procedures for both ${\mathsf{WGH}}_{\infty }$ and ${({\mathsf{GH}}_n)}_{0<n<\infty }$ that are based on particular sequents and on a set of proof rules dealing with such sequents. As these rules are strongly invertible the procedures naturally allow one to generate countermodels. Therefore we prove the decidability and the finite model property for these logics. Finally, from the decision procedure of ${\mathsf{WGH}}_{\infty }$, we design a sound and complete sequent calculus for this logic.     

Deontic Interpreted Systems

We investigate an extension of the formalism of interpreted systems by Halpern and colleagues to model the correct behaviour of agents. The semantical model allows for the representation and reasoning about states of correct and incorrect functioning behaviour of the agents, and of the system as a whole. We axiomatise this semantic class by mapping it into a suitable class of Kripke models. The resulting logic, KD45_n ^i-j, is a stronger version of KD, the system often referred to as Standard Deontic Logic. We extend this formal framework to include the standard epistemic notions defined on interpreted systems, and introduce a new doubly-indexed operator representing the knowledge that an agent would have if it operates under the assumption that a group of agents is functioning correctly. We discuss these issues both theoretically and in terms of applications, and present further directions of work.     

Extended Quantum Logic

The concept of quantum logic is extended so that it covers a more general set of propositions that involve non-trivial probabilities. This structure is shown to be embedded into a multi-modal framework, which has desirable logical properties such as an axiomatization, the finite model property and decidability.     

Some Supervaluation-based Consequence Relations

In this paper, we define some consequence relations based on supervaluation semantics for partial models, and we investigate their properties. For our main consequence relation, we show that natural versions of the following fail: upwards and downwards Lowenheim–Skolem, axiomatizability, and compactness. We also consider an alternate version for supervaluation semantics, and show both axiomatizability and compactness for the resulting consequence relation.     

Neighborhoods for Entailment

This paper presents a neighborhood semantics for logics of entailment. It begins with a minimal system Min that expresses the most fundamental assumptions about the entailment relation, and continues by examining various extensions that reflect further assumptions that might be made about entailment. This leads first to the logic B that is the basic relevant logic, and then to more powerful systems. All of these logics are proved to be sound and strongly complete. With B the neighborhood semantics meets the Routley–Meyer relational semantics for relevant logic; these connections are examined. The minimal and basic entailment logics are shown to have the finite model property, and hence to be decidable.