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Different models of judicial decision making highlight particular goals. Traditional legal theory posits that in making decisions judges strive to reach the correct legal decision as dictated by precedent. Attitudinal and strategic models focuses on the ways in which judges further their preferred policies. The managerial model emphasizes the increasing caseload pressures that judges at all levels face. Each model accurately captures some of what every judge does some of the time, but a sophisticated understanding of judicial decision making should explicitly incorporate the notion that judges simultaneously attempt to further numerous, disparate, and often conflicting, objectives. This chapter offers a preliminary account of a more psychologically plausible account of judicial cognition and motivation, based on principles of goal management in a constraint satisfaction network.

This chapter explores the algorithmic aspects of graph homomorphisms and of similar partition problems. The highlights include the dichotomy classification of graph homomorphisms to a fixed target graph $H$; a proof of the fact that dichotomy for digraph homomorphisms would imply dichotomy for all constraint satisfaction problems; a presentation of consistency-based algorithms; and associated dualities that seem to be applicable to all known polynomial cases of the digraph homomorphism problem. The role of polymorphisms in the design of polynomial algorithms is highlighted, and it is shown that graphs with the same set of polymorphisms define polynomially equivalent problems. The polymorphism known as the majority function is shown to yield a polynomial time homomorphism testing algorithm. The dichotomy classification of list homomorphism problems for reflexive graphs is presented. List matrix partition problems are posed in the language of trigraph homomorphisms, and the richness of the associated algorithms is illustrated on the case of clique cutsets and generalized split graphs.

This introductory chapter is a sampler of the material covered in the book. It introduces the notation and terminology in the book, and provides motivational examples and applications, many taken up in more detail in later chapters. It gives the flavour of combinatorial aspects, algorithmic aspects, retractions, duality, constraint satisfaction problems, as well as structural properties of homomorphism composition. The highlights of this chapter include a simple proof of the Colouring Interpolation Theorem, a generalization of the No-Homomorphism Lemma, the construction of a triangle-free graph to which all cubic triangle-free graphs are homomorphic, a case of the Edge Reconstruction Conjecture, and a generalization of a theorem of Frucht on graphs with prescribed automorphism groups.

This chapter describes five different constraint satisfaction problems. The first section introduces the idea of constraint satisfaction problems and presents a general way of solving them. Each of the five remaining sections takes on a different constraint satisfaction problem (Sudoku, cryptarithmetic, the eight-queens problem, logic problems, and scheduling) and shows how finding a solution can be cast as a computational task in Prolog.

The Chapter deals with methodological constraints and possibilities in employing experimental psychology towards an understanding of judging. While acknowledging the concern with the external-validity of the research, the Chapter cautions against adopting measures that would compromise its construct-validity and thus muddy up the conclusions to be drawn from the findings. At the same time, scholars of judging ought to cast a wide net to employ whichever valid research that speaks to the diverse set of mental operations involved in judging. The field should not shy away from utilizing germane basic-psychological findings, as long as they withstand the rigorous demands of external-validity. It is proposed that the body of research on coherence based reasoning is one such example. In sum, the Chapter advocates a pedantic attention to the experimental design of the research coupled with open-mindedness to the range of useful and valid methodologies.

Classic behavioral decision research has intensively explored deliberate processes in decision making. Accordingly, individuals are viewed as bounded rational actors who, because of cognitive limitations, use simple heuristics that are successful in certain environments. In this chapter, it is postulated that human cognitive capacity is less severely limited than has previously been assumed. When automatic processes are considered, one finds that cognitive capacity is not a binding constraint for many decision problems. The general parallel constraint satisfaction (PCS) approach is outlined, which aims at describing these automatic processes, and evidence supporting this approach is summarized. It is further argued, that in order to describe decision making comprehensively, models must account for the interaction between automatic and deliberate processes. The PCS rule is delineated which specifies this interaction. The model shifts the bounds of rationality considerably and has further evolutionary advantages. Implications for the efficient design of institutions are outlined. Finally, the German legal system is reviewed in terms of its ability to support efficient decision making by implementing many of the prescriptions derived from the PCS rule without explicit knowledge about the underlying processes.

This chapter applies the idea of constraint satisfaction to a form of thinking that seems much more natural and relaxed: visual interpretation. This is a type of thinking that everyone can do to some extent, typically with a lot less conscious effort than puzzles require. The first section briefly considers the concept of vision and its connection to thinking. The following sections examine a sampling of three visual interpretation tasks: the interpretation of an image of a two-dimensional terrain as seen from above (Section 6.2); the interpretation of the edges in an image of three-dimensional polyhedral objects (Section 6.3); and recognizing objects of interest in an image (Section 6.4).

Brains make minds because mental representations and processes are performed by neural mechanisms. Mental representations work by patterns of firing in neural groups. More complicated representations that go beyond sensory experience can be formed by binding representations together, combining patterns of firing into new ones. In particular, binding can produce semantic pointers that coalesce and compress different kinds of information, including sensory, motor, emotional and verbal information. Semantic pointers retain connections to sensory and motor experience while also acquiring the autonomy that is usually attributed to symbols. Eliasmith’s semantic pointer hypothesis shows how neural cells can interact to produce high-level thinking. Different representations compete with each other to provide accounts of what is going on in the world through a parallel process of satisfaction of multiple constraints. Neural networks can learn by changing the synaptic connections between neurons.

The cavity method is introduced as a heuristic framework from a physics perspective to solve probabilistic graphical models and is presented at both the replica symmetry (RS) and one-step replica symmetry breaking (1RSB) levels. This technique has been applied with success to a wide range of models and problems, such as spin glasses, random constraint satisfaction problems (rCSP), and error correcting codes. First, the RS cavity solution for the Sherrington–Kirkpatrick model—a fully connected spin glass model—is derived and its equivalence to the RS solution obtained using replicas is discussed. The general cavity method for diluted graphs is then illustrated at both RS and 1RSB levels. The latter was a significant breakthrough in the last decade and has direct applications to rCSP. Finally, as an example of an actual problem, k-SAT is investigated using belief and survey propagation.