This paper gives an outline of truthmaker semantics for natural language against the background of standard possible-worlds semantics. It develops a truthmaker semantics for attitude reports and deontic modals based on an ontology of attitudinal and modal objects and on a semantic function of clauses as predicates of such objects. It also présents new motivations for 'object-based truthmaker semantics' from intensional transitive verbs such as ‘need’, ‘look for’, ‘own’, and ‘buy’ and gives an outline of their semantics. This paper (...) is a commissioned 'target' article, with commentaries by W. Davis, B. Arsenijevic, K. Moulton, K. Liefke, M. Kaufmann, R. Matthews, P. Portner and A. Rubinstein, P. Elliott, G. Ramchand and my reply. (shrink)

In this paper we first develop a logic independent account of relevant implication. We propose a stipulative denition of what it means for a multiset of premises to relevantly L-imply a multiset of conclusions, where L is a Tarskian consequence relation: the premises relevantly imply the conclusions iff there is an abstraction of the pair such that the abstracted premises L-imply the abstracted conclusions and none of the abstracted premises or the abstracted conclusions can be omitted while still maintaining valid (...) L-consequence. Subsequently we apply this denition to the classical logic consequence relation to obtain NTR-consequence, i.e. the relevant CL-consequence relation in our sense, and develop a sequent calculus that is sound and complete with regard to relevant CL-consequence. We present a sound and complete sequent calculus for NTR. In a next step we add rules for an object language relevant implication to the sequent calculus. The object language implication reflects exactly the NTR-consequence relation. One can see the resulting logic NTR-> as a relevant logic in the traditional sense of the word. By means of a translation to the relevant logic R, we show that the presented logic NTR is very close to relevance logics in the Anderson-Belnap-Dunn-Routley-Meyer tradition. However, unlike usual relevant logics, NTR is decidable for the full language, Disjunctive Syllogism and Adjunction are valid, and neither Modus Ponens nor the Cut rule are admissible. (shrink)

We consider two‐variable, first‐order logic in which a single distinguished predicate is required to be interpreted as a transitive relation. We show that the finite satisfiability problem for this logic is decidable in triply exponential non‐deterministic time. Complexity falls to doubly exponential non‐deterministic time if the transitive relation is constrained to be a partial order.

This paper contains a proof-theoretic account of unification in transitive reflexive modal logics, which means that the reasoning is syntactic and uses as little semantics as possible. New proofs of theorems on unification types are presented and these results are extended to negationless fragments. In particular, a syntactic proof of Ghilardi’s result that $\mathsf {S4}$ has finitary unification is provided. In this approach the relation between classical valuations, projective unifiers, and admissible rules is clarified.

Recent work has brought to prominence the idea that some utterances contain occurrences of noun phrases that not only corefer, but do so in a particularly guaranteed or explicit way—call such occurrences ‘de jure coreferential’. Studies of de jure coreference have considered both the characteristics of the relation, and its explanation. Pinillos (154(2):301–324, 2011) argues that de jure coreference is non-transitive, and uses this as part of his argument for a new semantic primitive explaining de jure coreference. In this (...) paper, I draw attention to a neglected distinction between de jure coreference and another kind of coreference with which it might easily be confused. I then consider Pinillos’s claim that de jure coreference is non-transitive, and conclude that even using Pinillos’s definition of de jure coreference, it is far from straightforward that he has demonstrated the non-transitivity of de jure coreference. I question whether Pinillos’s characterisation of de jure coreference is adequate, and offer a plausible alternative characterisation. I show that on this new characterisation, there is no evidence that the relation is non-transitive. (shrink)

This paper aims to argue for, else illustrate the epistemological significance of the use of non transitive similarity relations, mapping only to "types", as methodologically being on a par with the use of transitive similarity relations (equivalence relations), mapping as well to "predicates". -/- In this paper the sketch of an exact but simple geometrical model of the above construct is followed by mentioning respective use cases for non transitive similarity relations from science and humanities. A well (...) known metaphysics example is elaborated along these lines to some extent. (shrink)

We prove that any positive elementary (least fixed point) induction expressing the negation of transitive closure on finite nondirected graphs requires at least two recursion variables.

The development of abstract schemas and productive rules in language is affected by both token and type frequencies. High token frequencies and surface similarities help to discover formal and functional commonalities between utterances and categorize them as instances of the same schema. High type frequencies and diversity help to develop slots in these schemas, which allow the production and comprehension of novel utterances. In the current study we looked at both token and type frequencies in two related constructions in German (...) child-directed speech: simple transitive and complement-clause constructions. Both constructions contain high frequency verbs, which potentially support the development of verb-specific schemas. However, only the frequent verbs in the transitive constructions occur with a variety of subject types, which also supports the development of a slot in the subject position. We then used an elicited production task to compare 4- and 5-year-old German-speaking children's productivity with simple transitive constructions and complement-clause constructions. The children were prompted to change the subjects of high and low frequency simple transitive verbs, such as essen ‘eat’ and naschen ‘nibble’, mental-state complement-taking verbs, such as denken ‘think’ and vermuten ‘presume’, and communication complement-taking verbs, such as sagen ‘say’ and berichten ‘report’. In accordance with earlier findings, children had less difficulty producing new utterances with high frequency transitive verbs than with low frequency transitive verbs. For the other verb classes, however, we found either reverse frequency effects or no frequency effects. For these verb classes, children's productivity can be determined by diversity rather than simple token frequency. We discuss how token frequency interacts with diversity, discourse function, semantic complexity, and syntactic complexity. (shrink)

Ethical voice involves individuals’ perceptions of what is right and what is wrong. Although prior research has investigated the impacts of individual-level prohibitive ethical expression on personal outcomes, there has been limited examination of ethical voice at the group level. Our study examines how and when different types of ethical voice influence group outcomes. Using data gathered from 363 participants from 61 groups in two Chinese companies, the results reveal that promotive and prohibitive ethical voices at the group level exert (...) opposing influences on group moral transitive motivation. Group moral transitive motivation serves as a mediating factor in the association between the two types of ethical voice and group ethical behaviors (GEB). In addition, group faultlines moderate the impact of promotive ethical voice and prohibitive ethical voice on group moral transitive motivation and on GEB (via group moral transitive motivation). Our study extends the focus of research from a single type of ethical voice at the individual level to multiple types at the group level. The findings contribute to the body of knowledge regarding group ethical voice (GEV) by articulating its mediating mechanism as well as its boundary condition. This research provides valuable insights for researchers and managers by offering a comprehensive understanding about the role of different types of GEV and how to reform GEV. (shrink)

We introduce a new logical operator CSTC and show that incorporating this operator into first-order logic enables as to capture the complexity class PSPACE. We also show that by varying how the operator is applied we can capture the complexity classes P, NP, the classes of the Polynomial Hierarchy PH, and PSPACE. As such, the operator CSTC can be regarded as a general purpose operator. We also give applications of these characterizations by showing that P and NP coincide with those (...) problems accepted by two new classes of program schemes , by producing some new complete problems for various complexity classes where the reductions are from first principles and do not use known complete problems , and by giving a simple proof that first-order logic incorporated with the least fixed point operator captures P. (shrink)

We consider the problem of the existence of uniform interpolants in the modal logic K4. We first prove that all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square}$$\end{document}-free formulas have uniform interpolants in this logic. In the general case, we shall prove that given a modal formula \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\phi}$$\end{document} and a sublanguage L of the language of the formula, we can decide whether \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} (...) \setlength{\oddsidemargin}{-69pt} \begin{document}$${\phi}$$\end{document} has a uniform interpolant with respect to L in K4. The \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square}$$\end{document}-free case is proved using a reduction to the Gödel Löb Logic GL, while in the general case we prove that the question of whether a modal formula has uniform interpolants over transitive frames can be reduced to a decidable expressivity problem on the μ-calculus. (shrink)

This paper tests a novel implication of the original version of prospect theory (Kahneman and Tversky, 1979): that choices may systematically violate transitivity. Some have interpreted this implication as a weakness, viewing it as an anomaly generated by the ‘editing phase’ of prospect theory which can be rendered redundant by an appropriate re-specification of the preference function. Although there is some existing evidence that transitivity fails descriptively, the particular form of non-transitivity implied by prospect theory is quite distinctive and hence (...) presents an ideal opportunity to expose that theory to test. An experiment is reported which reveals strong evidence of the predicted intransitivity. It is argued that the existence of this new form of non-transitive behaviour presents a fresh theoretical challenge to those seeking descriptively adequate theories of choice behaviour, and a particular challenge to those who seek explanations within the conventional economic paradigm of utility maximisation. (shrink)

The problem of unification in a normal modal logic $L$ can be defined as follows: given a formula $\varphi$, determine whether there exists a substitution $\sigma$ such that $\sigma $ is in $L$. In this paper, we prove that for several non-symmetric non-transitive modal logics, there exists unifiable formulas that possess no minimal complete set of unifiers.

Transitive inference (TI) refers to social cognition that facilitates the discernment of unknown relationships between individuals using known relationships. It is extensively reported that TI evolves in animals living in a large group because TI could assess relative rank without deducing all dyadic relationships, which averts costly fights. The relationships in a large group become so complex that social cognition may not be developed adequately to handle such complexity. If members apply TI to all possible members in the group, (...) TI requires extremely highly developed cognitive abilities especially in a large group. Instead of developing cognitive abilities significantly, animals may apply simplified TI we call reference TI in this study as heuristic approaches. The reference TI allows members to recognize and remember social interactions only among a set of reference members rather than all potential members. Our study assumes that information processes in the reference TI comprises (1) the number of reference members based on which individuals infer transitively, (2) the number of reference members shared by the same strategists, and (3) memory capacity. We examined how information processes evolve in a large group using evolutionary simulations in the hawk–dove game. Information processes with almost any numbers of reference members could evolve in a large group as long as the numbers of shared reference member are high because information from the others’ experiences is shared. TI dominates immediate inference, which assesses relative rank on direct interactions, because TI could establish social hierarchy more rapidly applying information from others’ experiences. (shrink)

There is a mistake in the definition of the covering criterion on page 6.

I discuss the question: Is it possible to prepare, by purely thermodynamic means, an ensemble described by a quantum state having a definite phase relation between two component states which have never been in direct contact? Resolution of this question requires us to take explicit account of the nature of the correlations between the system and its thermal environment.

We show that given a finite, transitive and reflexive Kripke model 〈 W , ≼, ⟦ ⋅ ⟧ 〉 and $${w \in W}$$ , the property of being simulated by w (i.e., lying on the image of a literalpreserving relation satisfying the ‘forth’ condition of bisimulation) is modally undefinable within the class of S4 Kripke models. Note the contrast to the fact that lying in the image of w under a bi simulation is definable in the standard modal language (...) even over the class of K4 models, a fairly standard result for which we also provide a proof. We then propose a minor extension of the language adding a sequent operator $${\natural}$$ (‘tangle’) which can be interpreted over Kripke models as well as over topological spaces. Over finite Kripke models it indicates the existence of clusters satisfying a specified set of formulas, very similar to an operator introduced by Dawar and Otto. In the extended language $${{\sf L}^+ = {\sf L}^{\square\natural}}$$ , being simulated by a point on a finite transitive Kripke model becomes definable, both over the class of (arbitrary) Kripke models and over the class of topological S4 models. As a consequence of this we obtain the result that any class of finite, transitive models over finitely many propositional variables which is closed under simulability is also definable in L + , as well as Boolean combinations of these classes. From this it follows that the μ -calculus interpreted over any such class of models is decidable. (shrink)

Suppose you are presented with three red objects. You are then asked to take a careful look at each possible pair of objects, and to decide whether or not their members look chromatically the same. You carry out the instructions thoroughly, and the following propositions sum up the results of your empirical investigation: <blockquote> i. red object #1 looks the same in colour as red object #2. </blockquote> ii. red object #2 looks the same in colour as red object #3.

According to William Craig, the notion of explanatory priority is the Achilles' heel of Robert Adams' argument against Molinism. Specifically, Craig contends that (1) the notion of explanatory priority is employed equivocally in the argument; (2) Adams is guilty of conflating reasons and causes; and (3) one of the intermediate conclusions of the argument is invalidly inferred, as can be seen by a counterexample. I argue that Craig is mistaken on all counts, and that Adams' argument emerges unscathed.

Natural conditions are provided that are sufficient to ensure that causality as defined by approaches that use counterfactual dependence and structural equations will be transitive.

We consider the classification problem for several classes of countable structures which are “vertex-transitive”, meaning that the automorphism group acts transitively on the elements. We show that the classification of countable vertex-transitive digraphs and partial orders are Borel complete. We identify the complexity of the classification of countable vertex-transitive linear orders. Finally we show that the classification of vertex-transitive countable tournaments is properly above \ in complexity.

In this paper we prove that thek-ary fragment of transitive closure logic is not contained in the extension of the (k−1)-ary fragment of partial fixed point logic by all (2k−1)-ary generalized quantifiers. As a consequence, the arity hierarchies of all the familiar forms of fixed point logic are strict simultaneously with respect to the arity of the induction predicates and the arity of generalized quantifiers.Although it is known that our theorem cannot be extended to the sublogic deterministic transitive (...) closure logic, we show that an extension is possible when we close this logic under congruence. (shrink)

The finite model property (FMP) in weakly transitive tense logics is explored. Let \(\mathbb {S}=[\textsf{wK}_t\textsf{4}, \textsf{K}_t\textsf{4}]\) be the interval of tense logics between \(\textsf{wK}_t\textsf{4}\) and \(\textsf{K}_t\textsf{4}\). We introduce the modal formula \(\textrm{t}_0^n\) for each \(n\ge 1\). Within the class of all weakly transitive frames, \(\textrm{t}_0^n\) defines the class of all frames in which every cluster has at most _n_ irreflexive points. For each \(n\ge 1\), we define the interval \(\mathbb {S}_n=[\textsf{wK}_t\textsf{4T}_0^{n+1}, \textsf{wK}_t\textsf{4T}_0^{n}]\) which is a subset of \(\mathbb {S}\). (...) There are \(2^{\aleph _0}\) logics in \(\mathbb {S}_n\) lacking the FMP, and there are \(2^{\aleph _0}\) logics in \(\mathbb {S}_n\) having the FMP. Then we explore the FMP in finitely alternative tense logics \(L_{n,m}=L\oplus \{\textrm{Alt}_n^F, \textrm{Alt}_m^P\}\) with \(n,m\ge 0\) and \(L\in \mathbb {S}\). For all \(k\ge 0\) and \(n,m\ge 1\), we define intervals \(\mathbb {F}^k_{n,m}\), \(\mathbb {P}^k_{n,m}\) and \(\mathbb {S}^k_{n,m}\) of tense logics. The number of logics lacking the FMP in them is either 0 or \(2^{\aleph _0}\), and the number of logics having the FMP in them is either finite or \(2^{\aleph _0}\). (shrink)

We examine schoolchildren’s reasoning with spatial relations, such as ‘is to the left of’. Our aims are to obtain a more precise account of the effect of working memory on reasoning, a more detaile...