Gentzen-type axiomatization for PAL

AbstractThe aim of propositional algorithmic logic (PAL) is to investigate the properties of simple nondeterministic while-program schemes on propositional level. We present finite, cut-free, Gentzen-type axiomatization of PAL. As a corollary from completeness theorem, we obtain the small-model theorem and algorithm for checking the validity of PAL formulas

Complexity and Expressivity of Branching- and Alternating-Time Temporal Logics with Finitely Many Variables

We show that Branching-time temporal logics CTL and CTL*, as well as Alternating-time temporal logics ATL and ATL*, are as semantically expressive in the language with a single propositional variable as they are in the full language, i.e., with an unlimited supply of propositional variables. It follows that satisfiability for CTL, as well as for ATL, with a single variable is EXPTIME-complete, while satisfiability for CTL*, as well as for ATL*, with a single variable is 2EXPTIME-complete,--i.e., for these logics, the satisfiability for formulas with only one variable is as hard as satisfiability for arbitrary formulas.Comment: Prefinal version of the published pape

Logic, Rational Agency, and Intelligent Interaction

... make a plea for recasting logic as a theory of interactive agency, and show how this perspective fits both old achievements and new broader ambitions for the field

Review of I Am a Strange Loop by Douglas Hofstadter (2007) (review revised 2019)

Latest Sermon from the Church of Fundamentalist Naturalism by Pastor Hofstadter. Like his much more famous (or infamous for its relentless philosophical errors) work Godel, Escher, Bach, it has a superficial plausibility but if one understands that this is rampant scientism which mixes real scientific issues with philosophical ones (i.e., the only real issues are what language games we ought to play) then almost all its interest disappears. I provide a framework for analysis based in evolutionary psychology and the work of Wittgenstein (since updated in my more recent writings). Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019

Bayesian Logic Programs

Bayesian networks provide an elegant formalism for representing and reasoning about uncertainty using probability theory. Theyare a probabilistic extension of propositional logic and, hence, inherit some of the limitations of propositional logic, such as the difficulties to represent objects and relations. We introduce a generalization of Bayesian networks, called Bayesian logic programs, to overcome these limitations. In order to represent objects and relations it combines Bayesian networks with definite clause logic by establishing a one-to-one mapping between ground atoms and random variables. We show that Bayesian logic programs combine the advantages of both definite clause logic and Bayesian networks. This includes the separation of quantitative and qualitative aspects of the model. Furthermore, Bayesian logic programs generalize both Bayesian networks as well as logic programs. So, many ideas developedComment: 52 page

The propositional nature of human associative learning

The past 50 years have seen an accumulation of evidence suggesting that associative learning depends oil high-level cognitive processes that give rise to propositional knowledge. Yet, many learning theorists maintain a belief in a learning mechanism in which links between mental representations are formed automatically. We characterize and highlight the differences between the propositional and link approaches, and review the relevant empirical evidence. We conclude that learning is the consequence of propositional reasoning processes that cooperate with the unconscious processes involved in memory retrieval and perception. We argue that this new conceptual framework allows many of the important recent advances in associative learning research to be retained, but recast in a model that provides a firmer foundation for both immediate application and future research