Therefore, our work alliances through multiple means: diplomatic, economic, seeks to advance capabilities in explainable AI/ML to allow conventional and unconventional warfare, including information a human operative to'calibrate their trust' in an AI/ML asset warfare. A critical requirement for allies is potentially provided by a different coalition partner (Tomsett rapid and continuous integration of capabilities to collect, et al. 2020). The purpose of human-machine teaming is process, disseminate and exploit actionable information and to aim for each party to exploit the strengths of, and compensate intelligence. To achieve this, the MDO layered ISR concept for the weaknesses of, the other (Cummings 2014).

Recently, the notions of subjective constraint monotonicity, epistemic splitting, and foundedness have been introduced for epistemic logic programs, with the aim to use them as main criteria respectively intuitions to compare different answer set semantics proposed in the literature on how they comply with these intuitions. In this note, we consider these three notions and demonstrate on some examples that they may be too strong in general and may exclude some desired answer sets respectively world views. In conclusion, these properties should not be regarded as mandatory properties that every answer set semantics must satisfy in general.

Weighted First Order Model Counting (WFOMC) computes the weighted sum of the models of a first order theory on a domain of a given finite size. WFOMC has emerged as a fundamental tool for probabilistic inference. Algorithms for WFOMC that run in polynomial time w.r.t. the domain size are called lifted inference algorithms. Such algorithms have been developed for multiple extensions of FO$^2$(the fragment of First Order Logic with two variables) for the special case of symmetric weight functions. In this paper, instead of developing a specific algorithm, we derive a closed form formula for WFOMC in FO$^2$. The three key advantages of our proposal are: (i) it deals with existential quantifiers without introducing negative weights; (ii) it easily extends to FO$^2$ with cardinality constraints and counting quantifiers (aka C$^2$); finally, (iii) it supports WFOMC for a class of weight functions strictly larger than symmetric weight functions, which can model count distributions, without introducing complex or negative weights.

We provide a comprehensive analysis of the computational complexity of the outcome determination problem for the most important aggregation rules proposed in the literature on logic-based judgment aggregation. Judgment aggregation is a powerful and flexible framework for studying problems of collective decision making that has attracted interest in a range of disciplines, including Legal Theory, Philosophy, Economics, Political Science, and Artificial Intelligence. The problem of computing the outcome for a given list of individual judgments to be aggregated into a single collective judgment is the most fundamental algorithmic challenge arising in this context. Our analysis applies to several different variants of the basic framework of judgment aggregation that have been discussed in the literature, as well as to a new framework that encompasses all existing such frameworks in terms of expressive power and representational succinctness.

In programming languages and type theory, polymorphism is the provision of a single interface to entities of different types[1] or the use of a single symbol to represent multiple different types.[2] Interest in polymorphic type systems developed significantly in the 1960s, with practical implementations beginning to appear by the end of the decade. Ad hoc polymorphism and parametric polymorphism were originally described in Christopher Strachey's Fundamental Concepts in Programming Languages[4], where they are listed as "the two main classes" of polymorphism. Ad hoc polymorphism was a feature of Algol 68, while parametric polymorphism was the core feature of ML's type system. In a 1985 paper, Peter Wegner and Luca Cardelli introduced the term inclusion polymorphism to model subtypes and inheritance,[2] citing Simula as the first programming language to implement it. Christopher Strachey chose the term ad hoc polymorphism to refer to polymorphic functions that can be applied to arguments of different types, but that behave differently depending on the type of the argument to which they are applied (also known as function overloading or operator overloading).[5]

This paper presents a novel approach for automated analysis of process models discovered using process mining techniques. Process mining explores underlying processes hidden in the event data generated by various devices. Our proposed Inductive machine learning method was used to build business process models based on actual event log data obtained from a hotel's Property Management System (PMS). The PMS can be considered as a Multi Agent System (MAS) because it is integrated with a variety of external systems and IoT devices. Collected event log combines data on guests stay recorded by hotel staff, as well as data streams captured from telephone exchange and other external IoT devices. Next, we performed automated analysis of the discovered process models using formal methods. Spin model checker was used to simulate process model executions and automatically verify the process model. We proposed an algorithm for the automatic transformation of the discovered process model into a verification model. Additionally, we developed a generator of positive and negative examples. In the verification stage, we have also used Linear temporal logic (LTL) to define requested system specifications. We find that the analysis results will be well suited for process model repair.

Generally, negation-limited inverters problem is known as a puzzle of constructing an inverter with AND gates and OR gates and a few inverters. In this paper, we introduce a curious new result about the effectiveness of two powerful ATP (Automated Theorem Proving) strategies on tackling negation limited inverter problem. Two resolution strategies are UR (Unit Resulting) resolution and hyper-resolution. In experiment, we come two kinds of automated circuit construction: 3 input/output inverters and 4 input/output BCD Counter Circuit. Both circuits are constructed with a few limited inverters. Curiously, it has been turned out that UR resolution is drastically faster than hyper-resolution in the measurement of the size of SOS (Set of Support). Besides, we discuss the syntactic and semantic criteria which might causes considerable difference of computation cost between UR resolution and hyper-resolution.

In this work we introduce a 3-valued logic with modalities, with the aim of having a clear and precise representation of epistemic states, thus the formulas of this logic will be our epistemic states. Indeed, these formulas are identified with ranking functions of 3 values, a generalization of total preorders of three levels. In this framework we analyze some types of changes of these epistemic structures and give syntactical characterizations of them in the introduced logic. In particular, we introduce and study carefully a new operator called Cautious Improvement operator. We also characterize all operators that are definable in this framework.

Our interest is in scientific problems with the following characteristics: (1) Data are naturally represented as graphs; (2) The amount of data available is typically small; and (3) There is significant domain-knowledge, usually expressed in some symbolic form. These kinds of problems have been addressed effectively in the past by Inductive Logic Programming (ILP), by virtue of 2 important characteristics: (a) The use of a representation language that easily captures the relation encoded in graph-structured data, and (b) The inclusion of prior information encoded as domain-specific relations, that can alleviate problems of data scarcity, and construct new relations. Recent advances have seen the emergence of deep neural networks specifically developed for graph-structured data (Graph-based Neural Networks, or GNNs). While GNNs have been shown to be able to handle graph-structured data, less has been done to investigate the inclusion of domain-knowledge. Here we investigate this aspect of GNNs empirically by employing an operation we term "vertex-enrichment" and denote the corresponding GNNs as "VEGNNs". Using over 70 real-world datasets and substantial amounts of symbolic domain-knowledge, we examine the result of vertex-enrichment across 5 different variants of GNNs. Our results provide support for the following: (a) Inclusion of domain-knowledge by vertex-enrichment can significantly improve the performance of a GNN. That is, the performance VEGNNs is significantly better than GNNs across all GNN variants; (b) The inclusion of domain-specific relations constructed using ILP improves the performance of VEGNNs, across all GNN variants. Taken together, the results provide evidence that it is possible to incorporate symbolic domain knowledge into a GNN, and that ILP can play an important role in providing high-level relationships that are not easily discovered by a GNN.

Robustly learning in expressive languages with real-world data continues to be a challenging task. Numerous conventional methods appeal to heuristics without any assurances of robustness. While PAC-Semantics offers strong guarantees, learning explicit representations is not tractable even in a propositional setting. However, recent work on so-called "implicit" learning has shown tremendous promise in terms of obtaining polynomial-time results for fragments of first-order logic. In this work, we extend implicit learning in PAC-Semantics to handle noisy data in the form of intervals and threshold uncertainty in the language of linear arithmetic. We prove that our extended framework keeps the existing polynomial-time complexity guarantees. Furthermore, we provide the first empirical investigation of this hitherto purely theoretical framework. Using benchmark problems, we show that our implicit approach to learning optimal linear programming objective constraints significantly outperforms an explicit approach in practice.