Binary Modality Research Articles

On undecidability of the propositional logic of an associative binary modality

It is shown that both classical and intuitionistic propositional logics of an associative binary modality are undecidable. The proof is based on the deduction theorem for these logics.

Modal Information Logics: Axiomatizations and Decidability

The present paper studies formal properties of so-called modal information logics (MILs)—modal logics first proposed in (van Benthem 1996) as a way of using possible-worlds semantics to model a theory of information. They do so by extending the language of propositional logic with a binary modality defined in terms of being the supremum of two states. First proposed in 1996, MILs have been around for some time, yet not much is known: (van Benthem 2017, 2019) pose two central open problems, namely (1) axiomatizing the two basic MILs of suprema on preorders and posets, respectively, and (2) proving (un)decidability. The main results of the first part of this paper are solving these two problems: (1) by providing an axiomatization [with a completeness proof entailing the two logics to be the same], and (2) by proving decidability. In the proof of the latter, an emphasis is put on the method applied as a heuristic for proving decidability ‘via completeness’ for semantically introduced logics; the logics lack the FMP w.r.t. their classes of definition, but not w.r.t. a generalized class. These results are build upon to axiomatize and prove decidable the MILs attained by endowing the language with an ‘informational implication’—in doing so a link is also made to the work of (Buszkowski 2021) on the Lambek Calculus.

An epistemic logic of preferences

The article studies preferences of agents in a setting with imperfect information. For such a setting, the authors propose a new class of preferences. It is said that an agent prefers one statement over another if, among all indistinguishable worlds, the agent prefers the worlds where the first statement is true to those where the second one is true. The main technical result is a sound and complete logical system describing the interplay between a binary modality capturing preferences and the knowledge modality. The proof of completeness is using a newly proposed “tumbled pairs” technique.

Boron Neutron Capture Therapy: Clinical Application and Research Progress.

Boron neutron capture therapy (BNCT) is a binary modality that is used to treat a variety of malignancies, using neutrons to irradiate boron-10 (10B) nuclei that have entered tumor cells to produce highly linear energy transfer (LET) alpha particles and recoil 7Li nuclei (10B [n, α] 7Li). Therefore, the most important part in BNCT is to selectively deliver a large number of 10B to tumor cells and only a small amount to normal tissue. So far, BNCT has been used in more than 2000 cases worldwide, and the efficacy of BNCT in the treatment of head and neck cancer, malignant meningioma, melanoma and hepatocellular carcinoma has been confirmed. We collected and collated clinical studies of second-generation boron delivery agents. The combination of different drugs, the mode of administration, and the combination of multiple treatments have an important impact on patient survival. We summarized the critical issues that must be addressed, with the hope that the next generation of boron delivery agents will overcome these challenges.

Monotone Subintuitionistic Logic: Duality and Transfer Results

We consider subintuitionistic logics as an extension of positive propositional logic with a binary modality, interpreted over ordered and unordered monotone neighborhood frames, with a range of frame conditions. This change in perspective allows us to apply tools and techniques from the modal setting to subintuitionistic logics. We provide a Priestley-style duality, and transfer results from the (classical) logic of monotone neighborhood frames to obtain completeness, conservativity, and a finite model property for the basic logic, extended with a number of axioms.

Experimental studies for the personalized application of boron neutron capture therapy to the treatment of cutaneous melanoma

Background: Boron neutron capture therapy (BNCT) is a binary modality based on the nuclear reaction 10B (n, α) lithium-7 (7Li) that has been used to treat a variety of tumors, among these, cutaneous melanoma (CM). In previous boron biodistribution studies in agreement with the personalized oncology, we have demonstrated that boronophenylalanine (BPA) uptake can be correlated with the tumoral temperature and viability. The main aim of these studies was to evaluate the relationship between tumoral temperature and the response to the complete BNCT.

Intestinal Akkermansia muciniphila predicts overall survival in advanced non-small cell lung cancer patients treated with anti-PD-1 antibodies: Results a phase II study.

9019 Background: The gut microbiome, most specifically centered on one of the most prevalent anaerobic bacterium Akkermansia muciniphila (Akk), has emerged as a potential hallmark of clinical benefit to ICI. The goal of this study was to validate the prognostic significance of Akk in advanced NSCLC patients amenable to ICI. Methods: The multicentric prospective observational study enrolled patients with advanced NSCLC amenable to single agent ICI in first and second line. Stool sample was collected at study entry. Primary end-point was investigator-assessed objective response rate (ORR). We considered that a meaningful clinical difference would correlate to a 10% ORR increase in the Akk-Pos group compared to the Akk-Neg group. At least 292 patients equally divided each in each group would be required for a power at 80% and a two-sided alpha level of 5%. Results: From Dec 2015 to Nov 2019, a total of 409 patients were screened and 311 patients enrolled across 12 academic centers in France and Canada. Median age was 64yr, 32% were female, 77% had non-squamous NSCLC and PD-L1 was ≥1% in 70% of the 213 assessable samples. Akk was detectable in 158 (51%) and absent in 153 (49%) patients. Baseline characteristics were well balanced between the two groups. When considering Akk-Pos vs Akk-Neg groups the primary endpoint ORR was 27% and 17% respectively ( p = 0.04). Rates of partial response, stable disease and progressive disease (PD) were 62%, 50% and 46% respectively in the Akk-Pos group compared to 38%, 50% and 54% in the Akk-Neg group ( p = 0.04). Moreover, 57% of patients were still alive after 12 months in the Akk-Pos group vs 43% in the Akk-Neg group ( p = 0.04). Microbiome profiling demonstrated that Akk-Pos group was associated with increase bacterial diversity and enrichment of Ruminococcus, Alistipes and Eubacterium. When considering the variations of the relative abundance of Akk within the Akk-Pos group, we obtained a large interval ranging from 0.0022% up to 64.78% with a 75th percentile at 4.42%. The relative abundance of Akk within > 0% to < 4.42% range in stools at diagnosis was associated with increased ORR, overall survival (OS) in multivariate analysis, independent of PD-L1 expression and ECOG. This sub-group was associated with more inflamed tumors with upregulation of CD3e, IfngTH1 and Vcam-1. Conversely, patients with overrepresentation of Akk > 4.42% experienced more PD and shorter OS. Antibiotic use was associated with a shift in favor of Gammaproteobacteria, enrichment of Akk ( > 4.42%) and shorter OS. Conclusions: We validated the prognostic role of Akk in patients with NSCLC. Stratification based on Akk relative abundance represents a more accurate independent predictor than the binary modality. Our study provides the rationale to develop microbiome-based approach to study gut dysbiosis in routine clinical oncology care. Clinical trial information: NCT04567446.

Gentrifying Climate Change: Ecological Modernisation and the Cultural Politics of Definition

Gentrifying Climate Change: Ecological Modernisation and the Cultural Politics of Definition

A duration calculus with neighborhood modalities

To reason about continuous processes in some areas of artificial intelligence and embedded systems one has to express real-time properties. For such purpose a real-time logic has to be considered. Various such logics have been proposed. Some of these formalisms interpret formulas over intervals of time. These are called interval logics. Zhou Chaochen and Michael Hansen have introduced one such first-order interval logic called Neighborhood Logic (NL) which has two expanding modalities ◊r and ◊l. They have shown the adequacy of these modalities by deriving other unary and binary modalities from them; in particular, they show that chop can be expressed in terms of these modalities. The logic is subsequently expanded to get a Duration Calculus (called DC/NL) by expressing temporal variables as integrals of state variables. Liveness and fairness properties of a computing system can now be expressed in DC/NL by means of neighborhood (expanding) modalities. We take up an investigation of DC/NL in detail. We present a proof system for it. We further show that most of the results that hold in the original Duration Calculus continue to hold in our logic with some modifications. In this process we discuss soundness, completeness, and decidability results for DC/NL. Thus this paper establishes DC/NL as a useful formalism for specifying and verifying properties of real-time computing systems.

UNCOMFORTABLE RESIDUES OF DIS-LOCATIA: MIGRATION AND MODERN PANJABI SHORT STORIES

Movement of peoples can be seen as a defining hallmark of the twentieth century, but the aftermath of these movements rarely falls under the critical eye of the intellectual. This paper collides and interprets the affects of two historical movements of people: the division of Panjab in 1947 and the migration to Canada from Panjab after the Green Revolution. I understand the process of movement in these contexts as a disturbance and therefore violent in nature. Through my reading of the stories Tobha Tek Singh, by Saadat Hasan Manto, Baraf da Geet, by Sadhu Binning, and Do Tapu, by Jarnail Singh I seek to understand the migration alternately than the Freudian distinction of Heimlich/Unheimlich. Away from a binary modality and unbeknownst to an interstitiality, I seek to put forward the term Dis-locatia, as a term that emerges from an engagement with the disorienting émigré pose that describes a haunted dispossessed space of searching occupied by émigré authors.

In vivo 19F MRI and 19F MRS of 19F-labelled boronophenylalanine–fructose complex on a C6 rat glioma model to optimize boron neutron capture therapy (BNCT)

Boron neutron capture therapy (BNCT) is a promising binary modality used to treat malignant brain gliomas. To optimize BNCT effectiveness a non-invasive method is needed to monitor the spatial distribution of BNCT carriers in order to estimate the optimal timing for neutron irradiation. In this study, in vivo spatial distribution mapping and pharmacokinetics evaluation of the 19F-labelled boronophenylalanine (BPA) were performed using 19F magnetic resonance imaging (19F MRI) and 19F magnetic resonance spectroscopy (19F MRS). Characteristic uptake of 19F–BPA in C6 glioma showed a maximum at 2.5 h after compound infusion as confirmed by both 19F images and 19F spectra acquired on blood samples collected at different times after infusion. This study shows the ability of 19F MRI to selectively map the bio-distribution of 19F–BPA in a C6 rat glioma model, as well as providing a useful method to perform pharmacokinetics of BNCT carriers.

A complete fuzzy logical system to deal with trust management systems

In this paper we approach trust management systems in a fuzzy logical setting. The idea is to provide a generalization of the classical framework, where trust is understood via the dichotomy “true–false”. In order to overcome the classical approach proposed by Weeks, following the ideas used by Hájek, Esteva, Godo and others to deal with probability, possibility, and necessity in a many-valued logical setting, we introduce the modal logic FTn(ŁΠ12) built up over the many-valued logic ŁΠ12. In particular, we enlarge the ŁΠ12 language by means of a binary modality says acting on pairs (pi,ϕ) of principals and assertions, where a principal is a propositional variable and an assertion is a propositional formula of a suited many-valued logic. The idea is to regard the evaluation of the modal formula says(pi,ϕ) as the degree of confidence the principalpiputs in the assertionϕ. For FTn(ŁΠ12) we introduce a syntax, a semantic and we show completeness. Then we discuss the validity of generalized modus ponens rule in our setting. Finally we deal with a Pavelka-style extension of our logic, and we also extend FTn(ŁΠ12) to allow principals to be hierarchically organized.

Logic of subtyping

We introduce new modal logical calculi that describe subtyping properties of Cartesian product and disjoint union type constructors as well as mutually recursive types defined using those type constructors. Basic logic of subtyping S extends classical propositional logic by two new binary modalities ⊗ and ⊕ . An interpretation of S is a function that maps standard connectives into set-theoretical operations (intersection, union, and complement) and modalities into Cartesian product and disjoint union type constructors. This allows S to capture many subtyping properties of the above type constructors. We also consider logics S ρ and S ρ ω that incorporate into S mutually recursive types over arbitrary and well-founded universes correspondingly. The main results are completeness of the above three logics with respect to appropriate type universes. In addition, we prove Cut elimination theorem for S and establish decidability of S and S ρ ω .

On Modal Logics of Partial Recursive Functions

The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to partial recursive function type constructor under the above interpretation. The cases of deterministic and non-deterministic functions are considered and for both of them semantically complete modal logics are described and decidability of these logics is established.

A decidable multi-modal logic of context

We give a logic for formulas φ−∘ ψ, with the informal reading “ ψ is true in the context described by φ”. These are interpreted as binary modalities, by quantification over an enumerable set of unary modalities c−∘ ψ, meaning “ ψ is true in context c”. The logic allows arbitrary nesting of contexts. A corresponding axiomatic presentation is given, and proven to be decidable, sound, and complete. Previously, quantificational logic of context restricted the nesting of contexts, and was only known to be decidable in very special cases.

A Cut-Free Sequent System for the Smallest Interpretability Logic

The idea of interpretability logics arose in Visser [Vis90]. He introduced the logics as extensions of the provability logic GLwith a binary modality ▸. The arithmetic realization of A ▸ B in a theory T will be that T plus the realization of B is interpretable in T plus the realization of A (T + A interprets T + B). More precisely, there exists a function f (the relative interpretation) on the formulas of the language of T such that T + B ⊢ C implies T + A ⊢ f(C). The interpretability logics were considered in several papers. An arithmetic completeness of the interpretability logic ILM, obtained by adding Montagna's axiom to the smallest interpretability logic IL, was proved in Berarducci [Ber90] and Shavrukov [Sha88] (see also Hajek and Montagna [HM90] and Hajek and Montagna [HM92]). [Vis90] proved that the interpretability logic ILP, an extension of IL, is also complete for another arithmetic interpretation. The completeness with respect to Kripke semantics due to Veltman was, for IL, ILMand ILP, proved in de Jongh and Veltman [JV90]. The fixed point theorem of GLcan be extended to ILand hence ILMand ILP(cf. de Jongh and Visser [JV91]). The unary pendant "T interprets T + A" is much less expressive and was studied in de Rijke [Rij92]. For an overview of interpretability logic, see Visser [Vis97], and Japaridze and de Jongh [JJ98]. In this paper, we give a cut-free sequent system for IL. To begin with, we give a cut-free system for the sublogic IL4of IL, whose ▸-free fragment is the modal logic K4. A cut-elimination theorem for ILis proved using the system for IK4and a property of Lob's axiom.

Completeness of neighbourhood logic

This paper presents a completeness result for a first-order interval temporal logic, called Neighbourhood Logic (NL) which has two neighbourhood modalities. NL can support the specification of liveness and fairness properties of computing systems as well as formalisation of many concepts of real analysis. These two modalities are also adequate in the sense that they can derive other important unary and binary modalities of interval temporal logic. We prove the completeness result for NL by giving a Kripke model semantics and then mapping the Kripke models to the interval models for NL.

Decidable and undecidable logics with a binary modality

We give an overview of decidability results for modal logics having a binary modality. We put an emphasis on the demonstration of proof-techniques, and hope that this will also help in finding the borderlines between decidable and undecidable fragments of usual first-order logic.