A Complete and Consistent Formal System for Sortals

A formal logical system for sortal quantifiers, sortal identity and (second order) quantification over sortal concepts is formulated. The absolute consistency of the system is proved. A completeness proof for the system is also constructed. This proof is relative to a concept of logical validity provided by a semantics, which assumes as its philosophical background an approach to sortals from a modern form of conceptualism.     

A Modal Sortal Logic

An intensional semantic system for languages containing, in their logical syntax, sortal quantifiers, sortal identities, (second-order) quantifiers over sortals and the necessity operator is constructed. This semantics provides non-standard assignments to predicate expressions, which diverge in kind from the entities assigned to sortal terms by the same semantic system. The nature of the entities assigned to predicate expressions shows, at the same time, that there is an internal semantic connection between those expressions and sortal terms. A formal logical system is formulated that is proved to be absolutely consistent, sound and complete with respect to the intensional semantic system.     

A Two Dimensional Tense-modal Sortal Logic

We consider a formal language whose logical syntax involves both modal and tense propositional operators, as well as sortal quantifiers, sortal identities and (second order) quantifiers over sortals. We construct an intensional semantics for the language and characterize a formal logical system which we prove to be sound and complete with respect to the semantics. Conceptualism is the philosophical background of the semantic system.     

Decidable Cases of First-order Temporal Logic with Functions

We consider the decision problem for cases of first-order temporal logic with function symbols and without equality. The monadic monodic fragment with flexible functions can be decided with EXPSPACE-complete complexity. A single rigid function is sufficient to make the logic not recursively enumerable. However, the monadic monodic fragment with rigid functions, where no two distinct terms have variables bound by the same quantifier, is decidable and EXPSPACE-complete. Presented by Robert Goldblatt     

Equality and Monodic First-Order Temporal Logic

It has been shown recently that monodic first-order temporal logic without functional symbols but with equality is incomplete, i.e., the set of the valid formulae of this logic is not recursively enumerable. In this paper we show that an even simpler fragment consisting of monodic monadic two-variable formulae is not recursively enumerable.     

A Note on the Interpolation Property in Tense Logic

It is proved that all bimodal tense logics which contain the logic of the weak orderings and have unbounded depth do not have the interpolation property.     

数字表型视域下的健康数据确权：基于时间逻辑的展开

健康数据的价值生成具有历时性的特征。数据确权的空间逻辑意识到了健康数据的公共价值,但是忽略了这种公共价值的生成与彰显可能需要经历长时间的积累。提倡健康数据确权的时间逻辑,就是要克服空间逻辑在确权问题上的即时性思考。数据价值在时间链条上的延伸得益于对健康数据的关系性解读,数据的当前使用与未来使用表征为数据与多个主体之间的“依附”与“分离”,由此赋予了数据以新的时间性。这意味着健康数据确权需要将数据价值的未来面向考虑进来。在此基础上,时间逻辑的践行需要代际义务、团结伦理的引导,同时强化规则的预防功能。

     

A Temporal Semantics for Basic Logic

In the context of truth-functional propositional many-valued logics, Hájek’s Basic Fuzzy Logic BL [14] plays a major rôle. The completeness theorem proved in [7] shows that BL is the logic of all continuous t-norms and their residua. This result, however, does not directly yield any meaningful interpretation of the truth values in BL per se. In an attempt to address this issue, in this paper we introduce a complete temporal semantics for BL. Specifically, we show that BL formulas can be interpreted as modal formulas over a flow of time, where the logic of each instant is ?ukasiewicz, with a finite or infinite number of truth values. As a main result, we obtain validity with respect to all flows of times that are non-branching to the future, and completeness with respect to all finite linear flows of time, or to an appropriate single infinite linear flow of time. It may be argued that this reduces the problem of establishing a meaningful interpretation of the truth values in BL logic to the analogous problem for ?ukasiewicz logic.     

Sortals for Dummies

Advocates of sortal essentialism have argued that concepts like “thing” or “object” lack the unambiguous individuative criteria necessary to play the role of genuine sortals in reference. Instead, they function as “dummy sortals” which are placeholders or incomplete designations. In disqualifying apparent placeholder sortals, however, these philosophers have posed insuperable problems for accounts of childhood conceptual development. I argue that recent evidence in psychology demonstrates that children do possess simple or basic sortals of physical objects or things. I contend that these concepts provide the genuine individuative criteria necessary for reference. As a consequence, sortalism can be made compatible with the developmental facts of conceptual development.

A New Representation Theorem for Contranegative Deontic Logic

The logic of an ought operator O is contranegative with respect to an underlying preference relation if it satisfies the property Op & (¬p)(¬q) Oq. Here the condition that is interpolative ((p (pq) q) (q (pq) p)) is shown to be necessary and sufficient for all -contranegative preference relations to satisfy the plausible deontic postulates agglomeration (Op & OqO(p&q)) and disjunctive division (O(p&q) Op Oq).     

A Logic for Information Systems

A conception of an information system has been introduced by Pawlak. The study has been continued in works of Pawlak and Orlowska and in works of Vakarelov. They had proposed some basic relations and had constructed a formal system of a modal logic that describes the relations and some of their Boolean combinations. Our work is devoted to a generalization of this approach. A class of relation systems and a complete calculus construction method for these systems are proposed. As a corollary of our main result, our paper contains a solution of a Vakarelov's problem: how to construct a formal system that describes all the Boolean combinations of the basic relations.     

Cooperation,Knowledge, and Time: Alternating-time Temporal Epistemic Logic and its Applications

Branching-time temporal logics have proved to be an extraordinarily successful tool in the formal specification and verification of distributed systems. Much of their success stems from the tractability of the model checking problem for the branching time logic CTL, which has made it possible to implement tools that allow designers to automatically verify that systems satisfy requirements expressed in CTL. Recently, CTL was generalised by Alur, Henzinger, and Kupferman in a logic known as Alternating-time Temporal Logic (ATL). The key insight in ATL is that the path quantifiers of CTL could be replaced by cooperation modalities, of the form , where is a set of agents. The intended interpretation of an ATL formula is that the agents can cooperate to ensure that holds (equivalently, that have a winning strategy for ). In this paper, we extend ATL with knowledge modalities, of the kind made popular in the work of Fagin, Halpern, Moses, Vardi and colleagues. Combining these knowledge modalities with ATL, it becomes possible to express such properties as group can cooperate to bring about iff it is common knowledge in that . The resulting logic — Alternating-time Temporal Epistemic Logic (ATEL) — shares the tractability of model checking with its ATL parent, and is a succinct and expressive language for reasoning about game-like multiagent systems.     

A Proof System for Classical Logic

An operation on inferential rules, called H-operation, is used to minimize the axiom basis for classical logic.     

A Propositional Dynamic Logic with Qualitative Probabilities

This paper presents an -completeness theorem for a new propositional probabilistic logic, namely, the dynamic propositional logic of qualitative probabilities (D Q P), which has been introduced by the author as a dynamic extension of the logic of qualitative probabilities (Q P) introduced by Segerberg.