Marek Sergot's research while affiliated with Imperial College London and other places

This paper studies some normative relations that hold between actions, their preconditions and their effects, with particular attention to connecting what are often called ‘ought to be’ norms with ‘ought to do’ norms. We use a formal model based on a form of transition system called a ‘coloured labelled transition system’ (coloured LTS) introduced in a series of papers by Sergot and Craven. Those works have variously presented a formalism (an ‘action language’) nC+ for defining and computing with a (coloured) LTS, and another, separate formalism, a modal language interpreted on a (coloured) LTS used to express its properties. We consolidate these two strands. Instead of specifying the obligatory and prohibited states and transitions as part of the construction of a coloured LTS as in nC+, we represent norms in the modal language and use those to construct a coloured LTS from a given regular (uncoloured) one. We also show how connections between norms on states and norms on transitions previously treated as fixed constraints of a coloured LTS can instead be defined within the modal language used for representing norms.

How should a machine intelligence perform unsupervised structure discovery over streams of sensory input? One approach to this problem is to cast it as an apperception task. Here, the task is to construct an explicit interpretable theory that both explains the sensory sequence and also satisfies a set of unity conditions, designed to ensure that the constituents of the theory are connected in a relational structure. However, the original formulation of the apperception task had one fundamental limitation: it assumed the raw sensory input had already been parsed using a set of discrete categories, so that all the system had to do was receive this already-digested symbolic input, and make sense of it. But what if we don't have access to pre-parsed input? What if our sensory sequence is raw unprocessed information? The central contribution of this paper is a neuro-symbolic framework for distilling interpretable theories out of streams of raw, unprocessed sensory experience. First, we extend the definition of the apperception task to include ambiguous (but still symbolic) input: sequences of sets of disjunctions. Next, we use a neural network to map raw sensory input to disjunctive input. Our binary neural network is encoded as a logic program, so the weights of the network and the rules of the theory can be solved jointly as a single SAT problem. This way, we are able to jointly learn how to perceive (mapping raw sensory information to concepts) and apperceive (combining concepts into declarative rules).

The paper investigates how actual cause may be treated in ‘seeing to it that’ (‘stit’) logics, that is, determining when the actions of a particular agent, or a particular set of agents collectively, can be said to be the cause of a given outcome in given circumstances. There are two complementary problems: (1) the outcome is brought about by the actions of some set of agents and the task is to identify which of these agents are essential to that bringing about, and (2) the outcome depends partly on chance and the task is to identify which agents could have acted differently and thereby ensured a different outcome. The final part of the paper discusses briefly the need to account for causal and other dependences between the actions of agents, and how that might be done without abandoning the ‘stit’ framework altogether.KeywordsLogic of agencystitActual causationChancy causationJoint action

The paper tackles the problem of the relation between rights and obligations. Two examples of situations in which such a relation occurs are discussed. One concerns the abortion regulations in Polish law, the other one - a clash between freedom of expression and freedom of enterprise occurring in the context of discrimination. The examples are analysed and formalised using labelled transition systems in the nC+ framework. Rights are introduced to the system as procedures allowing for their fulfilment. Obligations are based on the requirement of cooperation in the realisa-tion of the goals of the agent that has a right. If the right of an agent cannot be fulfilled without an action of another agent, then that action is obligatory for that agent. If there are many potential contributors who are individually allowed to refuse, then the last of them is obliged to help when all the others have already refused. By means of formalisation this account of the relation under consideration is precisely expressed and shown consistent.

How should a machine intelligence perform unsupervised structure discovery over streams of sensory input? One approach to this problem is to cast it as an apperception task [1]. Here, the task is to construct an explicit interpretable theory that both explains the sensory sequence and also satisfies a set of unity conditions, designed to ensure that the constituents of the theory are connected in a relational structure. However, the original formulation of the apperception task had one fundamental limitation: it assumed the raw sensory input had already been parsed using a set of discrete categories, so that all the system had to do was receive this already-digested symbolic input, and make sense of it. But what if we don't have access to pre-parsed input? What if our sensory sequence is raw unprocessed information? The central contribution of this paper is a neuro-symbolic framework for distilling interpretable theories out of streams of raw, unprocessed sensory experience. First, we extend the definition of the apperception task to include ambiguous (but still symbolic) input: sequences of sets of disjunctions. Next, we use a neural network to map raw sensory input to disjunctive input. Our binary neural network is encoded as a logic program, so the weights of the network and the rules of the theory can be solved jointly as a single SAT problem. This way, we are able to jointly learn how to perceive (mapping raw sensory information to concepts) and apperceive (combining concepts into declarative rules).

One of the best known approaches to the logic of agency are the ‘stit’ (‘seeing to it that’) logics. Often, it is not the actions of an individual agent that bring about a certain outcome but the joint actions of a set of agents, collectively. Collective agency has received comparatively little attention in ‘stit’. The paper maps out several different forms, several different senses in which a particular set of agents, collectively, can be said to bring about a certain outcome, and examines how these forms can be expressed in ‘stit’ and stit-like logics. The outcome that is brought about may be unintentional, and perhaps even accidental; the account deliberately ignores aspects such as joint intention, communication between agents, awareness of other agents’ intentions and capabilities, even the awareness of another agent’s existence. The aim is to investigate what can be said about collective agency when all such considerations are ignored, besides mere consequences of joint actions. The account will be related to the ‘strictly stit’ of Belnap and Perloff ( Annals of Mathematics and Artificial Intelligence 9 (1–2), 25–48 1993) and their suggestions concerning ‘inessential members’ and ‘mere bystanders’. We will adjust some of those conjectures and distinguish further between ‘potentially contributing bystanders’ and ‘impotent bystanders’.

This paper attempts to answer a central question in unsupervised learning: what does it mean to “make sense” of a sensory sequence? In our formalization, making sense involves constructing a symbolic causal theory that both explains the sensory sequence and also satisfies a set of unity conditions. The unity conditions insist that the constituents of the causal theory – objects, properties, and laws – must be integrated into a coherent whole. On our account, making sense of sensory input is a type of program synthesis, but it is unsupervised program synthesis. Our second contribution is a computer implementation, the Apperception Engine, that was designed to satisfy the above requirements. Our system is able to produce interpretable human-readable causal theories from very small amounts of data, because of the strong inductive bias provided by the unity conditions. A causal theory produced by our system is able to predict future sensor readings, as well as retrodict earlier readings, and impute (fill in the blanks of) missing sensory readings, in any combination. In fact, it is able to do all three tasks simultaneously. We tested the engine in a diverse variety of domains, including cellular automata, rhythms and simple nursery tunes, multi-modal binding problems, occlusion tasks, and sequence induction intelligence tests. In each domain, we test our engine's ability to predict future sensor values, retrodict earlier sensor values, and impute missing sensory data. The Apperception Engine performs well in all these domains, significantly out-performing neural net baselines. We note in particular that in the sequence induction intelligence tests, our system achieved human-level performance. This is notable because our system is not a bespoke system designed specifically to solve intelligence tests, but a general-purpose system that was designed to make sense of any sensory sequence.

The Apperception Engine is an unsupervised learning system. Given a sequence of sensory inputs, it constructs a symbolic causal theory that both explains the sensory sequence and also satisfies a set of unity conditions. The unity conditions insist that the constituents of the theory - objects, properties, and laws - must be integrated into a coherent whole. Once a theory has been constructed, it can be applied to predict future sensor readings, retrodict earlier readings, or impute missing readings. In this paper, we evaluate the Apperception Engine in a diverse variety of domains, including cellular automata, rhythms and simple nursery tunes, multi-modal binding problems, occlusion tasks, and sequence induction intelligence tests. In each domain, we test our engine's ability to predict future sensor values, retrodict earlier sensor values, and impute missing sensory data. The engine performs well in all these domains, significantly outperforming neural net baselines and state of the art inductive logic programming systems. These results are significant because neural nets typically struggle to solve the binding problem (where information from different modalities must somehow be combined together into different aspects of one unified object) and fail to solve occlusion tasks (in which objects are sometimes visible and sometimes obscured from view). We note in particular that in the sequence induction intelligence tests, our system achieved human-level performance. This is notable because our system is not a bespoke system designed specifically to solve intelligence tests, but a general-purpose system that was designed to make sense of any sensory sequence.

This paper attempts to answer a central question in unsupervised learning: what does it mean to "make sense" of a sensory sequence? In our formalization, making sense involves constructing a symbolic causal theory that explains the sensory sequence and satisfies a set of unity conditions. This model was inspired by Kant's discussion of the synthetic unity of apperception in the Critique of Pure Reason. On our account, making sense of sensory input is a type of program synthesis, but it is unsupervised program synthesis. Our second contribution is a computer implementation, the Apperception Engine, that was designed to satisfy the above requirements. Our system is able to produce interpretable human-readable causal theories from very small amounts of data, because of the strong inductive bias provided by the Kantian unity constraints. A causal theory produced by our system is able to predict future sensor readings, as well as retrodict earlier readings, and "impute" (fill in the blanks of) missing sensory readings, in any combination. We tested the engine in a diverse variety of domains, including cellular automata, rhythms and simple nursery tunes, multi-modal binding problems, occlusion tasks, and sequence induction IQ tests. In each domain, we test our engine's ability to predict future sensor values, retrodict earlier sensor values, and impute missing sensory data. The Apperception Engine performs well in all these domains, significantly out-performing neural net baselines. We note in particular that in the sequence induction IQ tasks, our system achieved human-level performance. This is notable because our system is not a bespoke system designed specifically to solve IQ tasks, but a general purpose apperception system that was designed to make sense of any sensory sequence.

This paper formalizes part of the cognitive architecture that Kant develops in the Critique of Pure Reason. The central Kantian notion that we formalize is the rule. As we interpret Kant, a rule is not a declarative conditional stating what would be true if such and such conditions hold. Rather, a Kantian rule is a general procedure, represented by a conditional imperative or permissive, indicating which acts must or may be performed, given certain acts that are already being performed. These acts are not propositions; they do not have truth-values. Our formalization is related to the input/output logics, a family of logics designed to capture relations between elements that need not have truth-values. In this paper, we introduce KL3 as a formalization of Kant’s conception of rules as conditional imperatives and permissives. We explain how it differs from standard input/output logics, geometric logic, and first-order logic, as well as how it translates natural language sentences not well captured by first-order logic. Finally, we show how the various distinctions in Kant’s much-maligned Table of Judgements emerge as the most natural way of dividing up the various types and sub-types of rule in KL3. Our analysis sheds new light on the way in which normative notions play a fundamental role in the conception of logic at the heart of Kant’s theoretical philosophy.