Related papers: The logic behind desirable sets of things, and its…
For a set of nonnegative integers $A$, denote by $R_{A}(n)$ the number of unordered representations of the integer $n$ as the sum of two different terms from $A$. In this paper we partially describe the structure of the sets, which have…
We present a logical framework that enables us to define a formal theory of computational trust in which this notion is analysed in terms of epistemic attitudes towards the possible objects of trust and in relation to existing evidence in…
The theory of rational choice assumes that when people make decisions they do so in order to maximize their utility. In order to achieve this goal they ought to use all the information available and consider all the choices available to…
Linear approximations to the decision boundary of a complex model have become one of the most popular tools for interpreting predictions. In this paper, we study such linear explanations produced either post-hoc by a few recent methods or…
A model of knowledge representation is described in which propositional facts and the relationships among them can be supported by other facts. The set of knowledge which can be supported is called the set of cognitive units, each having…
Justification theory is a unifying framework for semantics of non-monotonic logics. It is built on the notion of a justification, which intuitively is a graph that explains the truth value of certain facts in a structure. Knowledge…
Model theoretic results such as Characterization and Definability give important information about different logics. It is well known that the proofs of those results for several modal logics have, somehow, the same 'taste'. A general proof…
Coalition Logic is an important logic in logical studies of strategic reasoning, whose models are concurrent game models. In this paper, first, we systematically discuss three assumptions of concurrent game models and argue that they are…
For models of concurrent and distributed systems, it is important and also challenging to establish correctness in terms of safety and/or liveness properties. Theories of distributed systems consider equivalences fundamental, since they (1)…
This paper presents a plausible reasoning system to illustrate some broad issues in knowledge representation: dualities between different reasoning forms, the difficulty of unifying complementary reasoning styles, and the approximate nature…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
Explaining the behaviour of intelligent systems will get increasingly and perhaps intractably challenging as models grow in size and complexity. We may not be able to expect an explanation for every prediction made by a brain-scale model,…
Game Logic is an excellent setting to study proofs-about-programs via the interpretation of those proofs as programs, because constructive proofs for games correspond to effective winning strategies to follow in response to the opponent's…
Several rules for social choice are examined from a unifying point of view that looks at them as procedures for revising a system of degrees of belief in accordance with certain specified logical constraints. Belief is here a social…
This paper presents a soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic. The latter interprets formulas as interactive computational problems, formalized as games…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
This paper introduces a space of variable lotteries and proves a constructive version of the expected utility theorem. The word ``constructive'' is used here in two senses. First, as in constructive mathematics, the logic underlying proofs…
Prioritized default reasoning has illustrated its rich expressiveness and flexibility in knowledge representation and reasoning. However, many important aspects of prioritized default reasoning have yet to be thoroughly explored. In this…
As suggested by the title, this paper is a survey of recent results and questions on the collection of computably enumerable sets under inclusion. This is not a broad survey but one focused on the author's and a few others' current…
We provide a formal, simple and intuitive theory of rational decision making including sequential decisions that affect the environment. The theory has a geometric flavor, which makes the arguments easy to visualize and understand. Our…