Loosely Guarded Fragment of First-Order Logic has the Finite Model Property

We show that the loosely guarded and packed fragments of first-order logic have the finite model property. We use a construction of Herwig and Hrushovski. We point out some consequences in temporal predicate logic and algebraic logic.     

Completeness and Cut-Elimination for First-Order Ideal Paraconsistent Four-Valued Logic

Studia Logica - In this study, we prove the completeness and cut-elimination theorems for a first-order extension F4CC of Arieli, Avron, and Zamansky’s ideal paraconsistent four-valued logic...     

Completeness of a Branching-Time Logic with Possible Choices

In this paper we present BTC, which is a complete logic for branchingtime whose modal operator quantifies over histories and whose temporal operators involve a restricted quantification over histories in a given possible choice. This is a technical novelty, since the operators of the usual logics for branching-time such as CTL express an unrestricted quantification over histories and moments. The value of the apparatus we introduce is connected to those logics of agency that are interpreted on branching-time, as for instance Stit Logics.     

Quantum Logic as a Fragment of Independence-Friendly Logic

The working assumption of this paper is that noncommuting variables are irreducibly interdependent. The logic of such dependence relations is the author's independence-friendly (IF) logic, extended by adding to it sentence-initial contradictory negation ¬ over and above the dual (strong) negation . Then in a Hilbert space turns out to express orthocomplementation. This can be extended to any logical space, which makes it possible to define the dimension of a logical space. The received Birkhoff and von Neumann quantum logic can be interpreted by taking their disjunction to be ¬(A & B). Their logic can thus be mapped into a Boolean structure to which an additional operator has been added.     

A Completeness Proof for a Logic with an Alternative Necessity Operator

We show the completeness of a Hilbert-style system LK defined by M. Valiev involving the knowledge operator K dedicated to the reasoning with incomplete information. The completeness proof uses a variant of Makinson's canonical model construction. Furthermore we prove that the theoremhood problem for LK is co-NP-complete, using techniques similar to those used to prove that the satisfiability problem for propositional S5 is NP-complete.     

On the Proof-Theory of two Formalisations of Modal First-Order Logic

We introduce a Gentzen-style modal predicate logic and prove the cut-elimination theorem for it. This sequent calculus of cut-free proofs is chosen as a proxy to develop the proof-theory of the logics introduced in [14, 15, 4]. We present syntactic proofs for all the metatheoretical results that were proved model-theoretically in loc. cit. and moreover prove that the form of weak reflection proved in these papers is as strong as possible.     

Irreflexive Modality in the Intuitionistic Propositional Logic and Novikov Completeness

A. Kuznetsov considered a logic which extended intuitionistic propositional logic by adding a notion of 'irreflexive modality'. We describe an extension of Kuznetsov's logic having the following properties: (a) it is the unique maximal conservative (over intuitionistic propositional logic) extension of Kuznetsov's logic; (b) it determines a new unary logical connective w.r.t. Novikov's approach, i.e., there is no explicit expression within the system for the additional connective; (c) it is axiomatizable by means of one simple additional axiom scheme.     

On the Algebraizability of the Implicational Fragment of Abelian Logic

In this paper we consider the implicational fragment of Abelian logic \({{{\sf A}_{\rightarrow}}}\) . We show that although the Abelian groups provide an semantics for the set of theorems of \({{{\sf A}_{\rightarrow}}}\) they do not for the associated consequence relation. We then show that the consequence relation is not algebraizable in the sense of Blok and Pigozzi (Mem Am Math Soc 77, 1989). In the second part of the paper, we investigate an extension of \({{{\sf A}_{\rightarrow}}}\) in the same language and having the same set of theorems and show that this new consequence relation is algebraizable with the Abelian groups as its equivalent algebraic semantics. Finally, we show that although \({{{\sf A}_{\rightarrow}}}\) is not algebraizable, it is order-algebraizable in the sense of Raftery (Ann Pure Appl Log 164:251–283, 2013).     

A Proof of Standard Completeness for Esteva and Godo's Logic MTL

In the present paper we show that any at most countable linearly-ordered commutative residuated lattice can be embedded into a commutative residuated lattice on the real unit interval [0, 1]. We use this result to show that Esteva and Godo's logic MTL is complete with respect to interpretations into commutative residuated lattices on [0, 1]. This solves an open problem raised in.     

Completeness of Second-Order Intuitionistic Propositional Logic with Respect to Phase Semantics for Proof-Terms

Journal of Philosophical Logic - Girard introduced phase semantics as a complete set-theoretic semantics of linear logic, and Okada modified phase-semantic completeness proofs to obtain normal-form...     

A Defense of the Kripkean Account of Logical Truth in First-Order Modal Logic

This paper responds to criticism of the Kripkean account of logical truth in first-order modal logic. The criticism, largely ignored in the literature, claims that when the box and diamond are interpreted as the logical modality operators, the Kripkean account is extensionally incorrect because it fails to reflect the fact that all sentences stating truths about what is logically possible are themselves logically necessary. I defend the Kripkean account by arguing that some true sentences about logical possibility are not logically necessary.     

On the Standard and Rational Completeness of some Axiomatic Extensions of the Monoidal T-norm Logic

The monoidal t-norm based logic MTL is obtained from Hájek's Basic Fuzzy logic BL by dropping the divisibility condition for the strong (or monoidal) conjunction. Recently, Jenei and Montgana have shown MTL to be standard complete, i.e. complete with respect to the class of residuated lattices in the real unit interval [0,1] defined by left-continuous t-norms and their residua. Its corresponding algebraic semantics is given by pre-linear residuated lattices. In this paper we address the issue of standard and rational completeness (rational completeness meaning completeness with respect to a class of algebras in the rational unit interval [0,1]) of some important axiomatic extensions of MTL corresponding to well-known parallel extensions of BL. Moreover, we investigate varieties of MTL algebras whose linearly ordered countable algebras embed into algebras whose lattice reduct is the real and/or the rational interval [0,1]. These embedding properties are used to investigate finite strong standard and/or rational completeness of the corresponding logics.     

Two Kinds of Completeness and the Uses (and Abuses) of Exclusion Principles

I argue that the completeness of physics is composed of two distinct claims. The first is the commonly made claim that, roughly, every physical event is completely causally determined by physical events. The second has rarely, if ever, been explicitly stated in the literature and is the claim that microphysics provides a complete inventory of the fundamental categories that constitute both the causal features and intrinsic nature of all the events that causally affect the physical universe. After showing that these claims are distinct, I argue that they can be used to solve a difficulty with existing responses to the exclusion problem—namely, that these existing responses also undermine the powerful causal argument for physicalism. Recognizing that there are two kinds of completeness opens up room for the nonreductive physicalist to solve the exclusion problem while also endorsing a modified, cogent causal argument for a kind of physicalism compatible with her position.     

A New Normalization Strategy for the Implicational Fragment of Classical Propositional Logic

The introduction and elimination rules for material implication in natural deduction are not complete with respect to the implicational fragment of classical logic. A natural way to complete the system is through the addition of a new natural deduction rule corresponding to Peirce’s formula (((A → B) → A) → A). E. Zimmermann [6] has shown how to extend Prawitz’ normalization strategy to Peirce’s rule: applications of Peirce’s rule can be restricted to atomic conclusions. The aim of the present paper is to extend Seldin’s normalization strategy to Peirce’s rule by showing that every derivation Π in the implicational fragment can be transformed into a derivation Π′ such that no application of Peirce’s rule in Π′ occurs above applications of →-introduction and →-elimination. As a corollary of Seldin’s normalization strategy we obtain a form of Glivenko’s theorem for the classical {→}-fragment.     

Detour behaviour in three species of birds: quails (Coturnix sp.), herring gulls (Larus cachinnans) and canaries (Serinus canaria)

Detour behaviour is the ability of an animal to reach a goal stimulus by moving round any interposed obstacle. It has been widely studied and has been proposed as a test of insight learning in several species of mammals, but few data are available in birds. A comparative study in three species of birds, belonging to different eco-ethological niches, allows a better understanding of the cognitive mechanism of such detour behaviour. Young quails (Coturnix sp.), herring gulls (Larus cachinnans) and canaries (Serinus canaria), 1 month old, 10–25 days old and 4–6 months old, respectively, were tested in a detour situation requiring them to abandon a clear view of a biologically interesting object (their own reflection in a mirror) in order to approach that object. Birds were placed in a closed corridor, at one end of which was a barrier through which the object was visible. Four different types of barrier were used: vertical bar, horizontal bar, grid and transparent. Two symmetrical apertures placed midline in the corridor allowed the birds to adopt routes passing around the barrier. After entering the apertures, birds could turn either right or left to re-establish social contact with the object in the absence of any local sensory cues emanating from it. Quails appeared able to solve the task, though their performance depended on the type of barrier used, which appeared to modulate their relative interest in approaching the object or in exploring the surroundings. Young herring gulls also showed excellent abilities to locate spatially the out-of-view object, except when the transparent barrier was used. Canaries, on the other hand, appeared completely unable to solve the detour task, whatever barrier was in use. It is suggested that these species differences can be accounted for in terms of adaptation to a terrestrial or aerial environment.     

Peirce's Search for a Graphical Modal Logic (Propositional Part)

This paper deals with modality in Peirce's existential graphs, as expressed in his gamma and tinctured systems. We aim at showing that there were two philosophically motivated decisions of Peirce's that, in the end, hindered him from producing a modern, conclusive system of modal logic. Finally, we propose emendations and modifications to Peirce's modal graphical tinctured systems and to their underlying ideas that will produce modern modal systems.