The paper proposes a way to analyze logical reasoning in a deductive version of the Mastermind game implemented within the Math Garden educational system. Our main goal is to derive predictions about the cognitive difficulty of game-plays, e.g., the number of steps needed for solving the logical tasks or the working memory load. Our model is based on the analytic tableaux method, known from pro...

According to Aristotle, humans are the rational animal. The borderline between rationality and irrationality is fundamental to many aspects of human life including the law, mental health, and language interpretation. But what is it to be rational? One answer, deeply embedded in the Western intellectual tradition since ancient Greece, is that rationality concerns reasoning according to the rules...

We report on a series of experiments designed to test a new, unifying theory in psychology of deductive reasoning: mental metalogic (MML, for short; Yang & Bringsjord, 2001), which marks the unification of mental logic (ML) and mental model (MM) theory, and stands in part on the strength of empirical investigation of strategic interactions between logical syntactic and logical semantic processe...

In an effort to assess models of inductive reasoning and deductive reasoning, the authors, in 3 experiments, examined the effects of argument length and logical validity on evaluation of arguments. In Experiments 1a and 1b, participants were given either induction or deduction instructions for a common set of stimuli. Two distinct effects were observed: Induction judgments were more affected by...

A logical framework is a general meta-language for specifying and implementing deductive systems, given by axioms and inference rules. Based on a higher-order logic programming interpretation, it supports executing logical systems and reasoning with and about them, thereby reducing the effort required for each particular logical system. In this thesis, we describe different techniques to improv...

The framework of algorithmic knowledge assumes that agents use algorithms to compute the facts they explicitly know. In many cases of interest, a deductive system, rather than a particular algorithm, captures the formal reasoning used by the agents to compute what they explicitly know. We introduce a logic for reasoning about both implicit and explicit knowledge with the latter defined with res...

While reasoning with cases is usually done in a similaritybased manner, additional general knowledge is often represented in rules, constraints, or ontology definitions and is applied in a deductive reasoning process. This paper presents a new view on the combination of deductive and similarity-based reasoning, which is embedded in the CBR context. The basic idea is to view general knowledge an...

The aim of this paper is to propose dynamic logic as a cotmnon logical framework to describe and identify the most relevant formal characteristics of multi-language logical architectures (MLA) in order to investigate the expressive power of the knowledge bases that can be built upon them. In general, a MLA allows to build knowledge bases as a set of units with initial local theories written in ...