The semantics of rational contractions

This paper is concerned with the revision of beliefs in the face of new and possibly contradicting information. In the Logic of Theory Change developed by Alchourron, Gärdenfors and Makinson this nonmonotonic process consists of a contraction and an expansion of a set of formulas. to achieve minimal change they formulated widely accepted postulates that rational contractions have to fulfill. Contractions as defined by Alchourron, Gärdenfors and Makinson only operate on deductively closed sets of Formulas. Therefore they cannot be used in practical applications, eg. knowledge representation, where only finitely representable sets can be handled. We present a semantical characterization of rational finite contractions (the class of rational contractions maintaining finite representability) which provides an insight into the true nature of these operations. This characterization shows all possibilities to define concrete functions possessing these properties. When regarding concrete contractions known from literature in the light of our characterization we have found that they are all defined according to the same semantical strategy of minimal semantical change. As this strategy does not correspond to the goal of keeping as many important fotmulas as possible in the contracted set, we suggest a finite contraction defined according to the new strategy of maximal maintenance

The Sum-Product Algorithm For Quantitative Multiplicative Linear Logic

We consider an extension of multiplicative linear logic which encompasses bayesian networks and expresses samples sharing and marginalisation with the polarised rules of contraction and weakening. We introduce the necessary formalism to import exact inference algorithms from bayesian networks, giving the sum-product algorithm as an example of calculating the weighted relational semantics of a multiplicative proof-net improving runtime performance by storing intermediate results

Introduction to Cirquent Calculus and Abstract Resource Semantics

This paper introduces a refinement of the sequent calculus approach called cirquent calculus. While in Gentzen-style proof trees sibling (or cousin, etc.) sequents are disjoint sequences of formulas, in cirquent calculus they are permitted to share elements. Explicitly allowing or disallowing shared resources and thus taking to a more subtle level the resource-awareness intuitions underlying substructural logics, cirquent calculus offers much greater flexibility and power than sequent calculus does. A need for substantially new deductive tools came with the birth of computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html) - the semantically constructed formal theory of computational resources, which has stubbornly resisted any axiomatization attempts within the framework of traditional syntactic approaches. Cirquent calculus breaks the ice. Removing contraction from the full collection of its rules yields a sound and complete system for the basic fragment CL5 of computability logic. Doing the same in sequent calculus, on the other hand, throws out the baby with the bath water, resulting in the strictly weaker affine logic. An implied claim of computability logic is that it is CL5 rather than affine logic that adequately materializes the resource philosophy traditionally associated with the latter. To strengthen this claim, the paper further introduces an abstract resource semantics and shows the soundness and completeness of CL5 with respect to it.Comment: To appear in Journal of Logic and Computatio

Review of Making the Social World by John Searle (2010) (review revised 2019)

Before commenting in detail on making the Social World (MSW) I will first offer some comments on philosophy (descriptive psychology) and its relationship to contemporary psychological research as exemplified in the works of Searle (S) and Wittgenstein (W), since I feel that this is the best way to place Searle or any commentator on behavior, in proper perspective. It will help greatly to see my reviews of PNC, TLP, PI, OC, TARW and other books by these two geniuses of descriptive psychology. S makes no reference to W’s prescient statement of mind as mechanism in TLP, and his destruction of it in his later work. Since W, S has become the principal deconstructor of these mechanical views of behavior, and the most important descriptive psychologist (philosopher), but does not realize how completely W anticipated him nor, by and large, do others (but see the many papers and books of Proudfoot and Copeland on W, Turing and AI). S’s work is vastly easier to follow than W’s, and though there is some jargon, it is mostly spectacularly clear if you approach it from the right direction. See my reviews of W S and other books for more details. Overall, MSW is a good summary of the many substantial advances over Wittgenstein resulting from S’s half century of work, but in my view, W still is unequaled for basic psychology once you grasp what he is saying (see my reviews). Ideally, they should be read together: Searle for the clear coherent prose and generalizations on the operation of S2/S3, illustrated with W’s perspicacious examples of the operation of S1/S2, and his brilliant aphorisms. If I were much younger I would write a book doing exactly that. 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

Kripke Models for Classical Logic

We introduce a notion of Kripke model for classical logic for which we constructively prove soundness and cut-free completeness. We discuss the novelty of the notion and its potential applications