Representation choice is of fundamental importance to our ability to communicate and reason effectively. A major unsolved problem, addressed in this paper, is how to devise representational-system (RS) agnostic techniques that drive representation transformation and choice. We present a novel calculus, called structure transfer, that enables representation transformation across diverse RSs. Specifically, given a source representation drawn from a source RS, the rules of structure transfer allow us to generate a target representation for a target RS. The generality of structure transfer comes in part from its ability to ensure that the source representation and the generated target representation satisfy any specified relation (such as semantic equivalence). This is done by exploiting schemas, which encode knowledge about RSs. Specifically, schemas can express preservation of information across relations between any pair of RSs, and this knowledge is used by structure transfer to derive a structure for the target representation which ensures that the desired relation holds. We formalise this using Representational Systems Theory, building on the key concept of a construction space. The abstract nature of construction spaces grants them the generality to model RSs of diverse kinds, including formal languages, geometric figures and diagrams, as well as informal notations. Consequently, structure transfer is a system-agnostic calculus that can be used to identify alternative representations in a wide range of practical settings.

This paper seeks to apply categorical logic to the design of artificial intelligent agents that reason symbolically about objects more richly structured than sets. Using Johnstone's sequent calculus of terms- and formulae-in-context, we develop forward chaining and normal form algorithms for reasoning about objects in cartesian categories with the rules for Horn logic. We also adapt first-order unification to support multi-sorted theories, contexts, and fragments of first-order logic. The significance of these reformulations rests in the fact that they can be applied to reasoning about objects in semantic categories that do not support classical logic or even all its connectives.

Deep Learning experiments have critical requirements regarding the careful handling of their datasets as well as the efficient and correct usage of APIs that interact with hardware accelerators. On the one hand, software mistakes during data handling can contaminate experiments and lead to incorrect results. On the other hand, poorly coded APIs that interact with the hardware can lead to sub-optimal usage and untrustworthy conclusions. In this work we investigate the use of Linear Logic for the analysis of Deep Learning experiments. We show that primitives and operators of Linear Logic can be used to express: (i) an abstract representation of the control flow of an experiment, (ii) a set of available experimental resources, such as API calls to the underlying data-structures and hardware as well as (iii) reasoning rules about the correct consumption of resources during experiments. Our proposed model is not only lightweight but also easy to comprehend having both a symbolic and a visual component. Finally, its artifacts are themselves proofs in Linear Logic that can be readily verified by off-the-shelf reasoners.

Many works have studied the efficacy of state machines for detecting anomalies within NetFlows. These works typically learn a model from unlabeled data and compute anomaly scores for arbitrary traces based on their likelihood of occurrence or how well they fit within the model. However, these methods do not dynamically adapt their scores based on the traces seen at test time. This becomes a problem when an adversary produces seemingly common traces in their attack, causing the model to miss the detection by assigning low anomaly scores. We propose SEQUENT, a new approach that uses the state visit frequency to adapt its scoring for anomaly detection dynamically. SEQUENT subsequently uses the scores to generate root causes for anomalies. These allow the grouping of alarms and simplify the analysis of anomalies. Our evaluation of SEQUENT on three NetFlow datasets indicates that our approach outperforms existing methods, demonstrating its effectiveness in detecting anomalies.

In multiagent systems autonomous agents interact with each other to achieve individual and collective goals. Typical interactions concern negotiation and agreement on resource exchanges. Modeling and formalizing these agreements pose significant challenges, particularly in capturing the dynamic behaviour of agents, while ensuring that resources are correctly handled. Here, we propose exchange environments as a formal setting where agents specify and obey exchange policies, which are declarative statements about what resources they offer and what they require in return. Furthermore, we introduce a decidable extension of the computational fragment of linear logic as a fundamental tool for representing exchange environments and studying their dynamics in terms of provability.

We describe the methods and technologies underlying the application Grants4Companies. The application uses a logic-based expert system to display a list of business grants suitable for the logged-in business. To evaluate suitability of the grants, formal representations of their conditions are evaluated against properties of the business, taken from the registers of the Austrian public administration. The logical language for the representations of the grant conditions is based on S-expressions. We further describe a Proof of Concept implementation of reasoning over the formalised grant conditions. The proof of concept is implemented in Common Lisp and interfaces with a reasoning engine implemented in Scryer Prolog. The application has recently gone live and is provided as part of the Business Service Portal by the Austrian Federal Ministry of Finance.

We introduce a constructive method applicable to a large number of description logics (DLs) for establishing the concept-based Beth definability property (CBP) based on sequent systems. Using the highly expressive DL RIQ as a case study, we introduce novel sequent calculi for RIQ-ontologies and show how certain interpolants can be computed from sequent calculus proofs, which permit the extraction of explicit definitions of implicitly definable concepts. To the best of our knowledge, this is the first sequent-based approach to computing interpolants and definitions within the context of DLs, as well as the first proof that RIQ enjoys the CBP. Moreover, due to the modularity of our sequent systems, our results hold for any restriction of RIQ, and are applicable to other DLs by suitable modifications.

A new family of categorial grammars is proposed, defined by enriching basic categorial grammars with a conjunction operation. It is proved that the formalism obtained in this way has the same expressive power as conjunctive grammars, that is, context-free grammars enhanced with conjunction. It is also shown that categorial grammars with conjunction can be naturally embedded into the Lambek calculus with conjunction and disjunction operations. This further implies that a certain NP-complete set can be defined in the Lambek calculus with conjunction. We also show how to handle some subtle issues connected with the empty string. Finally, we prove that a language generated by a conjunctive grammar can be described by a Lambek grammar with disjunction (but without conjunction).

Quantum computing offers the potential for superior computational capabilities, particularly for data-intensive tasks. However, the current state of quantum hardware puts heavy restrictions on input size. To address this, hybrid transfer learning solutions have been developed, merging pre-trained classical models, capable of handling extensive inputs, with variational quantum circuits. Yet, it remains unclear how much each component -- classical and quantum -- contributes to the model's results. We propose a novel hybrid architecture: instead of utilizing a pre-trained network for compression, we employ an autoencoder to derive a compressed version of the input data. This compressed data is then channeled through the encoder part of the autoencoder to the quantum component. We assess our model's classification capabilities against two state-of-the-art hybrid transfer learning architectures, two purely classical architectures and one quantum architecture. Their accuracy is compared across four datasets: Banknote Authentication, Breast Cancer Wisconsin, MNIST digits, and AudioMNIST. Our research suggests that classical components significantly influence classification in hybrid transfer learning, a contribution often mistakenly ascribed to the quantum element. The performance of our model aligns with that of a variational quantum circuit using amplitude embedding, positioning it as a feasible alternative.

It is known that different categorial grammars have surface representation in a fragment of first order multiplicative linear logic (MLL1). We show that the fragment of interest is equivalent to the recently introduced extended tensor type calculus (ETTC). ETTC is a calculus of specific typed terms, which represent tuples of strings, more precisely bipartite graphs decorated with strings. Types are derived from linear logic formulas, and rules correspond to concrete operations on these string-labeled graphs, so that they can be conveniently visualized. This provides the above mentioned fragment of MLL1 that is relevant for language modeling not only with some alternative syntax and intuitive geometric representation, but also with an intrinsic deductive system, which has been absent. In this work we consider a non-trivial notationally enriched variation of the previously introduced ETTC, which allows more concise and transparent computations. We present both a cut-free sequent calculus and a natural deduction formalism.