Temporal Landscapes: A Graphical Temporal Logic for Reasoning

We present an elementary introduction to a new logic for reasoning about behaviors that occur over time. This logic is based on temporal type theory. The syntax of the logic is similar to the usual first-order logic; what differs is the notion of truth value. Instead of reasoning about whether formulas are true or false, our logic reasons about temporal landscapes. A temporal landscape may be thought of as representing the set of durations over which a statement is true. To help understand the practical implications of this approach, we give a wide variety of examples where this logic is used to reason about autonomous systems.Comment: 20 pages, lots of figure

A presentation theorem for continuous logic and Metric Abstract Elementary Classes

We give a presentation theorem for continuous first-order logic and Metric Abstract Elementary classes in terms of $L_{\omega_1, \omega}$ and Abstract Elementary Classes, respectively. This presentation is accomplished by analyzing dense subsets that are closed under functions. We extend this correspondence to types and saturation

Bisimulation in Inquisitive Modal Logic

Inquisitive modal logic, InqML, is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. Technically, InqML fits within the family of logics based on team semantics. From a model-theoretic perspective, it takes us a step in the direction of monadic second-order logic, as inquisitive modal operators involve quantification over sets of worlds. We introduce and investigate the natural notion of bisimulation equivalence in the setting of InqML. We compare the expressiveness of InqML and first-order logic, and characterise inquisitive modal logic as the bisimulation invariant fragments of first-order logic over various classes of two-sorted relational structures. These results crucially require non-classical methods in studying bisimulations and first-order expressiveness over non-elementary classes.Comment: In Proceedings TARK 2017, arXiv:1707.0825

Multitask Evolution with Cartesian Genetic Programming

We introduce a genetic programming method for solving multiple Boolean circuit synthesis tasks simultaneously. This allows us to solve a set of elementary logic functions twice as easily as with a direct, single-task approach.Comment: 2 page

Rules and derivations in an elementary logic course

When teaching an elementary logic course to students who have a general scientific background but have never been exposed to logic, we have to face the problem that the notions of deduction rule and of derivation are completely new to them, and are related to nothing they already know, unlike, for instance, the notion of model, that can be seen as a generalization of the notion of algebraic structure. In this note, we defend the idea that one strategy to introduce these notions is to start with the notion of inductive definition [1]. Then, the notion of derivation comes naturally. We also defend the idea that derivations are pervasive in logic and that defining precisely this notion at an early stage is a good investment to later define other notions in proof theory, computability theory, automata theory, ... Finally, we defend the idea that to define the notion of derivation precisely, we need to distinguish two notions of derivation: labeled with elements and labeled with rule names. This approach has been taken in [2]