Axioms for Deliberative Stit

Based on a notion of companions to stit formulas applied in other papers dealing with astit logics, we introduce choice formulas and nested choice formulas to prove the completeness theorems for dstit logics in a language with the dstit operator as the only non-truth-functional operator. The main logic discussed in this paper is the basic logic of dstit with multiple agents, other logics discussed include the basic logic of dstit with a single agent and some logics of dstit with multiple agents each of which corresponds to a semantic condition concerning the number of possible choices for agents.     

Labeled Calculi and Finite-Valued Logics

A general class of labeled sequent calculi is investigated, and necessary and sufficient conditions are given for when such a calculus is sound and complete for a finite-valued logic if the labels are interpreted as sets of truth values (sets-as-signs). Furthermore, it is shown that any finite-valued logic can be given an axiomatization by such a labeled calculus using arbitrary "systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is logarithmic in the number of truth values, and it is shown that this bound is tight.     

Embedding Logics into Product Logic

We construct a faithful interpretation of ukasiewicz's logic in product logic (both propositional and predicate). Using known facts it follows that the product predicate logic is not recursively axiomatizable.We prove a completeness theorem for product logic extended by a unary connective of Baaz [1]. We show that Gödel's logic is a sublogic of this extended product logic.We also prove NP-completeness of the set of propositional formulas satisfiable in product logic (resp. in Gödel's logic).     

Many-Valued Logics and Suszko's Thesis Revisited

Suszko's Thesis maintains that many-valued logics do not exist at all. In order to support it, R. Suszko offered a method for providing any structural abstract logic with a complete set of bivaluations. G. Malinowski challenged Suszko's Thesis by constructing a new class of logics (called q-logics by him) for which Suszko's method fails. He argued that the key for logical two-valuedness was the "bivalent" partition of the Lindenbaum bundle associated with all structural abstract logics, while his q-logics were generated by "trivalent" matrices. This paper will show that contrary to these intuitions, logical two-valuedness has more to do with the geometrical properties of the deduction relation of a logical structure than with the algebraic properties embedded on it.     

Varieties of Monadic Heyting Algebras. Part I

This paper deals with the varieties of monadic Heyting algebras, algebraic models of intuitionistic modal logic MIPC. We investigate semisimple, locally finite, finitely approximated and splitting varieties of monadic Heyting algebras as well as varieties with the disjunction and the existence properties. The investigation of monadic Heyting algebras clarifies the correspondence between intuitionistic modal logics over MIPC and superintuitionistic predicate logics and provides us with the solutions of several problems raised by Ono [35].     

On the Logic of Acceptance and Rejection

The logic of acceptance and rejection (AEL2) is a nonmonotonic formalism to represent states of knowledge of an introspective agent making decisions about available information. Though having much in common, AEL2 differs from Moore's autoepistemic logic (AEL) by the fact that the agent not only can accept or reject a given fact, but he/she also has the possibility not to make any decision in case he/she does not have enough knowledge.     

Rewording the Rules on Disjunctive Probability

Logic is a central and highly useful part of philosophy. Its value is particularly evident when it comes to keeping our thinking about disjunctive probabilities clear. Because of the two meanings of “or” (“just one of these statements is true,” “at least one of these statements is true”), logic can show how the likelihood of a disjunction being true can be determined quite easily. To gauge the chance that one of two or more exclusive alternatives is true, one need only sum up their respective likelihoods. And to know the chance that at least one of two or more compatible alternatives is true, one simply has to figure the chance that it is false that all of them are false!     

KAGAWA TOYOHIKO (1888–1960): WITNESS TO THE COSMIC DRAMA

At home and abroad, Kagawa Toyohiko was probably the best‐known Japanese Christian evangelist, social reformer, writer, and public intellectual of the twentieth century, nominated for the Nobel Prize in Literature twice (1947, 1948) and the Nobel Peace Prize three times (1954, 1955, 1956). Appealing to the masses with little knowledge of Christian faith, Kagawa believed that a positive, religio‐aesthetic interpretation of nature and science was a key missiological concern in Japan. He reasoned that a faith rooted in the kenotic movement of incarnation and self‐giving must strongly support the scientific quest. A voracious reader of science and especially biology, he argues for “directionality,” or what he calls “initial purpose” in the long, painful, cosmic journey from matter to life to mind (or consciousness). Through an antireductionistic, a posteriori methodological pluralism that sought to “see all things whole,” this “scientific mystic” employed Christian, Buddhist, Neo‐Confucian, personalist, and vitalist ideas to envision complementary roles for science and religion in modern society.