Nothing but the Truth

A curious feature of Belnap’s “useful four-valued logic”, also known as first-degree entailment (FDE), is that the overdetermined value B (both true and false) is treated as a designated value. Although there are good theoretical reasons for this, it seems prima facie more plausible to have only one of the four values designated, namely T (exactly true). This paper follows this route and investigates the resulting logic, which we call Exactly True Logic.     

On Gentzen Relations Associated with Finite-valued Logics Preserving Degrees of Truth

When considering m-sequents, it is always possible to obtain an m-sequent calculus VL for every m-valued logic (defined from an arbitrary finite algebra L of cardinality m) following for instance the works of the Vienna Group for Multiple-valued Logics. The Gentzen relations associated with the calculi VL are always finitely equivalential but might not be algebraizable. In this paper we associate an algebraizable 2-Gentzen relation with every sequent calculus VL in a uniform way, provided the original algebra L has a reduct that is a distributive lattice or a pseudocomplemented distributive lattice. We also show that the sentential logic naturally associated with the provable sequents of this algebraizable Gentzen relation is the logic that preserves degrees of truth with respect to the original algebra (in contrast with the more common logic that merely preserves truth). Finally, for some particular logics we obtain 2-sequent calculi that axiomatize the algebraizable Gentzen relations obtained so far.     

Gentzen Calculi for the Existence Predicate

We introduce Gentzen calculi for intuitionistic logic extended with an existence predicate. Such a logic was first introduced by Dana Scott, who provided a proof system for it in Hilbert style. We prove that the Gentzen calculus has cut elimination in so far that all cuts can be restricted to very simple ones. Applications of this logic to Skolemization, truth value logics and linear frames are also discussed.     

只有真实，才能得信，然后有力

某些主流媒体高调宣传《道德经》进大学课堂。这是什么样的大学的《道德经》“教材”呢多年来的事实告诉人们：伪学术、伪科学如果没有新闻媒体的鼓吹,特别是如果没有权威媒体、主流媒体的鼓吹,就形不成大气候,造不成大危害。因此,在反对伪学术、伪科学的同时,我们必须高度关注伪宣传和伪新闻问题。     

祛邪术就是骗人术

祛邪术是巫术的一种,花样繁多,源远流长.时至今日,在一些地方、一些人群中,祛邪活动还严重地存在着,甚至花样翻新.其手段虽各不相同,但有一点是相同的,那就是想祛邪却除不了害,想求福却反而遭灾.     

Protoalgebraic Gentzen Systems and the Cut Rule

In this paper we show that, in Gentzen systems, there is a close relation between two of the main characters in algebraic logic and proof theory respectively: protoalgebraicity and the cut rule. We give certain conditions under which a Gentzen system is protoalgebraic if and only if it possesses the cut rule. To obtain this equivalence, we limit our discussion to what we call regular sequent calculi, which are those comprising some of the structural rules and some logical rules, in a sense we make precise. We note that this restricted set of rules includes all the usual rules in the literature. We also stress the difference between the case of two-sided sequents and the case of many-sided sequents, in which more conditions are needed.     

DFC-algorithms for Suszko logic and one-to-one Gentzen type formalizations

We use here the notions and results from algebraic theory of programs in order to give a new proof of the decidability theorem for Suszko logic SCI (Theorem 3).We generalize the method used in the proof of that theorem in order to prove a more general fact that any prepositional logic which admits a cut-free Gentzen type formalization is decidable (Theorem 6).We establish also the relationship between the Suszko Logic SCI, one-to-one Gentzen type formalizations and deterministic and algorithmic regular languages (Remark 2 and Theorem 7, respectively).     

A Phenomenological Calculus for Anisotropic Systems

The phenomenological calculus is a relational paradigm for complex systems, closely related in substance and spirit to Robert Rosen’s own approach. Its mathematical language is multilinear algebra. The epistemological exploration continues in this paper, with the expansion of the phenomenological calculus into the realm of anisotropy.     

A Calculus of Substitutions for DPL

We consider substitutions in order sensitive situations, having in the back of our minds the case of dynamic predicate logic (DPL) with a stack semantics. We start from the semantic intuition that substitutions are move instructions on stacks: the syntactic operation [y/x] is matched by the instruction to move the value of the y-stack to the x-stack. We can describe these actions in the positive fragment of DPLE. Hence this fragment counts as a logic for DPL-substitutions. We give a calculus for the fragment and prove soundness and completeness.     

Nothing but the truth: self-disclosure, self-revelation, and the persona of the analyst

The question of the analyst's self-disclosure and self-revelation inhabits every moment of every psychoanalytic treatment. All self-disclosures and revelations, however, are not equivalent, and differentiating among them allows us to define a construct that can be called the analytic persona. Analysts already rely on an unarticulated concept of an analytic persona that guides them, for instance, as they decide what constitutes appropriate boundaries. Clinical examples illustrate how self-disclosures and revelations from within and without the analytic persona feel different, for both patient and analyst. The analyst plays a specific role for each patient and is both purposefully and unconsciously different in this context than in other settings. To a great degree, the self is a relational phenomenon. Our ethics call for us to tell nothing but the truth and simultaneously for us not to tell the whole truth. The unarticulated working concept of an analytic persona that many analysts have refers to the self we step out of at the close of each session and the self we step into as the patient enters the room. Attitudes toward self-disclosure and self-revelation can be considered reflections of how we conceptualize this persona.     

A Recommendation for Correspondence Theory of Truth

The purpose of this paper is to show that the correspondence theory as a truth-maker theory has certain advantages over some of the other theories of truth. The cost of this advantage is postulating extra entities—facts. However, the benefits outweigh the costs; facts facilitate our understanding of the nature of truth made by the world. Facts are required for understanding this world; therefore, one cannot claim that a separate cost is incurred for explaining truth. It is further argued that because of specific reasons the correspondence theory can be treated even better than the truth-maker theory and so the recommendation for correspondence as the most efficient theory of truth.

     

A Cut-Free Sequent Calculus for Defeasible Erotetic Inferences

In recent years, the effort to formalize erotetic inferences—i.e., inferences to and from questions—has become a central concern for those working in erotetic logic. However, few have sought to formulate a proof theory for these inferences. To fill this lacuna, we construct a calculus for (classes of) sequents that are sound and complete for two species of erotetic inferences studied by Inferential Erotetic Logic (IEL): erotetic evocation and erotetic implication. While an effort has been made to axiomatize the former in a sequent system, there is currently no proof theory for the latter. Moreover, the extant axiomatization of erotetic evocation fails to capture its defeasible character and provides no rules for introducing or eliminating question-forming operators. In contrast, our calculus encodes defeasibility conditions on sequents and provides rules governing the introduction and elimination of erotetic formulas. We demonstrate that an elimination theorem holds for a version of the cut rule that applies to both declarative and erotetic formulas and that the rules for the axiomatic account of question evocation in IEL are admissible in our system.