Signalling In Languages With Imperfect Information

This paper is a short survey of different languageswith imperfect information introduced in (Hintikka and Sandu 1989).The imperfect information concerns both quantifiers and connectives.At the end, I will sketch a connection between these languages and linearlogic.     

Imperfect Information in Pre-choice Screening of Options

Three experiments examined decision makers′ use of imperfect information in screening of decision options. It was found that: (1) when specific information about options was missing the absence was treated as a violation of the related decision criterion in the manner described by image theory (Beach, 1990; Beach & Mitchell, 1987) - rejection of options was a function of both the number of violations and the amount of missing information; (2) general paucity of information about options prompted rejection over and above the effects of violations, but paucity had about half the impact of violations or of missing information; (3) information about the probability that an option′s outcomes actually will occur were it the final choice was integrated additively with other information in screening, as predicted by image theory, and was integrated multiplicatively with other information in choice, as predicted by expected utility theory. Together with the results of previous research, these results support the image theory view of decision making as a two-stage process, screening followed by choice, and demonstrate once again the pivotal role of screening in this process.     

Two-Valued Logics of Intentionality: Temporality,Truth, Modality,and Identity

The essay introduces a non-Diodorean, non-Kantian temporal modal semantics based on part-whole, rather than class, theory. Formalizing Edmund Husserl’s theory of inner time consciousness, §3 uses his protention and retention concepts to define a relation of self-awareness on intentional events. §4 introduces a syntax and two-valued semantics for modal first-order predicate object-languages, defines semantic assignments for variables and predicates, and truth for formulae in terms of the axiomatic version of Edmund Husserl’s dependence ontology (viz. the Calculus [CU] of Urelements) introduced by The Ontology of Intentionality I & II. It then uses the §3 results to define the modalities of truth, and §5 extends the semantics to identity claims. §6 defines and contrasts synthetic a priori truths to analytic a priori truths, and §7 compares Brentano School noetic semantic and Leibnizian possible-world semantic perspectives on modality. The essay argues that the modal logics it defines semantically are two-valued, first-order versions of the type of language which Husserl viewed as the language of any ontology of experience (i.e. of any science), and conceived as the logic of intentionality.     

Identity without form: Abstract representations of letters

Subjects viewed single letters and orthographically regular pseudowords in a tachistoscope at threshold duration. The pseudowords were either all of one case (upper or lower) or they were of mixed case. Letter identity (“A”) and case judgments were required for one letter on each trial. It was found that letter identity was often reported correctly when case was reported incorrectly, even for letters whose upper- and lowercase forms are physically dissimilar (e.g., G-g). This “case effect” was stronger for letters in pseudowords than for letters presented alone. It held across different type fonts, and it occurred even when the upper-and lowercase letters were of different sizes (gEaT) and when the instructions to the subjects stressed the greater importance of case reports over identity reports. The results are consistent with the view that letter identification is an automatic process, the product of which is an abstract representation containing no information about physical form.     

Expressivity of Second Order Propositional Modal Logic

We consider second-order propositional modal logic (SOPML), an extension of the basic modal language with propositional quantifiers introduced by Kit Fine in 1970. We determine the precise expressive power of SOPML by giving analogues of the Van Benthem–Rosen theorem and the Goldblatt Thomason theorem. Furthermore, we show that the basic modal language is the bisimulation invariant fragment of SOPML, and we characterize the bounded fragment of first-order logic as being the intersection of first-order logic and SOPML.     

Expressivity results for deontic logics of collective agency

We use a deontic logic of collective agency to study reducibility questions about collective agency and collective obligations. The logic that is at the basis of our study is a multi-modal logic in the tradition of stit (‘sees to it that’) logics of agency. Our full formal language has constants for collective and individual deontic admissibility, modalities for collective and individual agency, and modalities for collective and individual obligations. We classify its twenty-seven sublanguages in terms of their expressive power. This classification enables us to investigate reducibility relations between collective deontic admissibility, collective agency, and collective obligations, on the one hand, and individual deontic admissibility, individual agency, and individual obligations, on the other.

     

Synchronization of Logics

Motivated by applications in software engineering, we propose two forms of combination of logics: synchronization on formulae and synchronization on models. We start by reviewing satisfaction systems, consequence systems, one-step derivation systems and theory spaces, as well as their functorial relationships. We define the synchronization on formulae of two consequence systems and provide a categorial characterization of the construction. For illustration we consider the synchronization of linear temporal logic and equational logic. We define the synchronization on models of two satisfaction systems and provide a categorial characterization of the construction. We illustrate the technique in two cases: linear temporal logic versus equational logic; and linear temporal logic versus branching temporal logic. Finally, we lift the synchronization on formulae to the category of logics over consequences systems.     

Logics of Synonymy

Journal of Philosophical Logic - We investigate synonymy in the strong sense of content identity (and not just meaning similarity). This notion is central in the philosophy of language and in...     

The Poset of All Logics III: Finitely Presentable Logics

Studia Logica - A logic in a finite language is said to be finitely presentable if it is axiomatized by finitely many finite rules. It is proved that binary non-indexed products of logics that are...     

非同一的统一:重新审视物质构成

在大卫像与大理石以及心与身之间的关系问题上,传统观点不是陷入同一论,就是沦落为某种形式的二元论。物质构成范畴作为一种"非同一的统一"关系,有望走出一条非还原的物理主义路线。一方面,根据模态论证,被构成的事物不是必然地同一于构成它的事物,在被构成的事物的本质上,构成观坚持了外在主义。另一方面,具有构成关系的两个事物,通过"双向"借入或派生,能够彼此共享模态属性以外的绝大部分属性,故不是二元分离而是相互统一的。物质构成作为一种新的哲学范畴有重要的形而上学和心灵哲学意义。     

Lottery Semantics: A Compositional Semantics for Probabilistic First-Order Logic with Imperfect Information

We present a compositional semantics for first-order logic with imperfect information that is equivalent to Sevenster and Sandu’s equilibrium semantics (under which the truth value of a sentence in a finite model is equal to the minimax value of its semantic game). Our semantics is a generalization of an earlier semantics developed by the first author that was based on behavioral strategies, rather than mixed strategies.     

Logics of Informational Interactions

The pre-eminence of logical dynamics, over a static and purely propositional view of Logic, lies at the core of a new understanding of both formal epistemology and the logical foundations of quantum mechanics. Both areas appear at first sight to be based on purely static propositional formalisms, but in our view their fundamental operators are essentially dynamic in nature. Quantum logic can be best understood as the logic of physically-constrained informational interactions (in the form of measurements and entanglement) between subsystems of a global physical system. Similarly, (multi-agent) epistemic logic is the logic of socially-constrained informational interactions (in the form of direct observations, learning, various forms of communication and testimony) between “subsystems” of a social system. Dynamic Epistemic Logic (DEL) provides us with a unifying setting in which these informational interactions, coming from seemingly very different areas of research, can be fully compared and analyzed. The DEL formalism comes with a powerful set of tools that allows us to make the underlying dynamic/interactive mechanisms fully transparent.     

Gentzenization of Trilattice Logics

Sequent calculi for trilattice logics, including those that are determined by the truth entailment, the falsity entailment and their intersection, are given. This partly answers the problems in Shramko-Wansing (J Philos Logic 34:121–153, 2005).     

On the Existence of Continua of Logics Between Some Intermediate Predicate Logics

A method for constructing continua of logics squeezed between some intermediate predicate logics, developed by Suzuki [8], is modified and applied to intervals of the form [L, L+ ¬¬S], where Lis a predicate logic, Sis a closed predicate formula. This solves one of the problems from Suzuki's paper.     

Logics of public communications

Multi-modal versions of propositional logics S5 or S4—commonly accepted as logics of knowledge—are capable of describing static states of knowledge but they do not reflect how the knowledge changes after communications among agents. In the present paper (part of broader research on logics of knowledge and communications) we define extensions of the logic S5 which can deal with public communications. The logics have natural semantics. We prove some completeness, decidability and interpretability results and formulate a general method that solves certain kind of problems involving public communications—among them well known puzzles of Muddy Children and Mr. Sum & Mr. Product. As the paper gives a formal logical treatment of the operation of restriction of the universe of a Kripke model, it contributes also to investigations of semantics for modal logics. This paper was originally published as Plaza, J. A. (1989). Logics of public communications. In M. L. Emrich, M. S. Pfeifer, M. Hadzikadic, & Z.W. Ras (Eds.), Proceedings of the fourth international symposium on methodologies for intelligent systems: Poster session program (pp. 201–216). Publisher: Oak Ridge National Laboratory, ORNL/DSRD-24. Research partly supported by NSF Grant CCR-8702307 and PSC-CUNY Grant 668283.     

Behavioral Algebraization of Logics

We introduce and study a new approach to the theory of abstract algebraic logic (AAL) that explores the use of many-sorted behavioral logic in the role traditionally played by unsorted equational logic. Our aim is to extend the range of applicability of AAL toward providing a meaningful algebraic counterpart also to logics with a many-sorted language, and possibly including non-truth-functional connectives. The proposed behavioral approach covers logics which are not algebraizable according to the standard approach, while also bringing a new algebraic perspective to logics which are algebraizable using the standard tools of AAL. Furthermore, we pave the way toward a robust behavioral theory of AAL, namely by providing a behavioral version of the Leibniz operator which allows us to generalize the traditional Leibniz hierarchy, as well as several well-known characterization results. A number of meaningful examples will be used to illustrate the novelties and advantages of the approach. Presented by Daniele Mundici     

Three-Dimensional Information in Face Representations Revealed by Identity Aftereffects

ABSTRACT— Representations of individual faces evolve with experience to support progressively more robust recognition. Knowledge of three-dimensional face structure is required to predict an image of a face as illumination and viewpoint change. Robust recognition across such transformations can be achieved with representations based on multiple two-dimensional views, three-dimensional structure, or both. We used face-identity adaptation in a familiarization paradigm to address a long-standing controversy concerning the role of two-dimensional versus three-dimensional information in face representations. We reasoned that if three-dimensional information is coded in the representations of familiar faces, then learning a new face using images generated by one three-dimensional transformation should enhance the robustness of the representation to another type of three-dimensional transformation. Familiarization with multiple views of faces enhanced the transfer of face-identity adaptation effects across changes in illumination by compensating for a generalization cost at a novel test viewpoint. This finding demonstrates a role for three-dimensional information in representations of familiar faces.