In Pietroski ( 2018 ) a simple representation language called SMPL is introduced, construed as a hypothesis about core conceptual structure. The present work is a study of this system from a logical perspective. In addition to establishing a completeness result and a complexity characterization for reasoning in the system, we also pinpoint its expressive limits, in particular showing that the fourth corner in the square of opposition (“ Some_not ”) eludes expression. We then study a seemingly small extension, called (...) SMPL +, which allows for a minimal predicate-binding operator. Perhaps surprisingly, the resulting system is shown to encode precisely the concepts expressible in first-order logic. However, unlike the latter class, the class of SMPL + expressions admits a simple procedural (context-free) characterization. Our contribution brings together research strands in logic—including natural logic, modal logic, description logic, and hybrid logic—with recent advances in semantics and philosophy of language. (shrink)

Theories of rational decision making often abstract away from computational and other resource limitations faced by real agents. An alternative approach known as resource rationality puts such matters front and center, grounding choice and decision in the rational use of finite resources. Anticipated by earlier work in economics and in computer science, this approach has recently seen rapid development and application in the cognitive sciences. Here, the theory of rationality plays a dual role, both as a framework for normative assessment (...) and as a source of scientific hypotheses about how mental processes in fact work. The latter project, often called rational analysis, depends for its success on a fine-grained characterization of the computational problem facing a decision maker, which may in turn depend on realistic assumptions about what the relevant agent is like. As a consequence, resource rationality involves a delicate, but often fruitful interplay between the normative and the descriptive. (shrink)

Existing research suggests that people's judgments of actual causation can be influenced by the degree to which they regard certain events as normal. We develop an explanation for this phenomenon that draws on standard tools from the literature on graphical causal models and, in particular, on the idea of probabilistic sampling. Using these tools, we propose a new measure of actual causal strength. This measure accurately captures three effects of normality on causal judgment that have been observed in existing studies. (...) More importantly, the measure predicts a new effect ("abnormal deflation"). Two studies show that people's judgments do, in fact, show this new effect. Taken together, the patterns of people's causal judgments thereby provide support for the proposed explanation. (shrink)

While Bayesian models have been applied to an impressive range of cognitive phenomena, methodological challenges have been leveled concerning their role in the program of rational analysis. The focus of the current article is on computational impediments to probabilistic inference and related puzzles about empirical confirmation of these models. The proposal is to rethink the role of Bayesian methods in rational analysis, to adopt an independently motivated notion of rationality appropriate for computationally bounded agents, and to explore broad conditions under (...) which Bayesian agents would be rational. The proposal is illustrated with a characterization of costs inspired by thermodynamics. (shrink)

While pragmatic arguments for numerical probability axioms have received much attention, justifications for axioms of qualitative probability have been less discussed. We offer an argument for the requirement that an agent’s qualitative judgments be probabilistically representable, inspired by, but importantly different from, the Money Pump argument for transitivity of preference and Dutch book arguments for quantitative coherence. The argument is supported by a theorem, to the effect that a subject is systematically susceptible to dominance given her preferred acts, if and (...) only if the subject’s comparative judgments preclude representation by a standard probability measure. (shrink)

The provability logic of a theory $T$ is the set of modal formulas, which under any arithmetical realization are provable in $T$. We slightly modify this notion by requiring the arithmetical realizations to come from a specified set $\Gamma$. We make an analogous modification for interpretability logics. We first study provability logics with restricted realizations and show that for various natural candidates of $T$ and restriction set $\Gamma$, the result is the logic of linear frames. However, for the theory Primitive (...) Recursive Arithmetic (PRA), we define a fragment that gives rise to a more interesting provability logic by capitalizing on the well-studied relationship between PRA and I$\Sigma_1$. We then study interpretability logics, obtaining upper bounds for IL(PRA), whose characterization remains a major open question in interpretability logic. Again this upper bound is closely related to linear frames. The technique is also applied to yield the nontrivial result that IL(PRA) $\subset$ ILM. (shrink)

We present a formal system for reasoning about inclusion and exclusion in natural language, following work by MacCartney and Manning. In particular, we show that an extension of the Monotonicity Calculus, augmented by six new type markings, is sufficient to derive novel inferences beyond monotonicity reasoning, and moreover gives rise to an interesting logic of its own. We prove soundness of the resulting calculus and discuss further logical and linguistic issues, including a new connection to the classes of weak, strong, (...) and superstrong negative polarity items. (shrink)

A well-known open problem in epistemic logic is to give a syntactic characterization of the successful formulas. Semantically, a formula is successful if and only if for any pointed model where it is true, it remains true after deleting all points where the formula was false. The classic example of a formula that is not successful in this sense is the “Moore sentence” p ∧ ¬BOXp, read as “p is true but you do not know p.” Not only is the (...) Moore sentence unsuccessful, it is self-refuting, for it never remains true as described. We show that in logics of knowledge and belief for a single agent (extended by S5), Moorean phenomena are the source of all self-refutation; moreover, in logics for an introspective agent (extending KD45), Moorean phenomena are the source of all unsuccessfulness as well. This is a distinctive feature of such logics, for with a non-introspective agent or multiple agents, non-Moorean unsuccessful formulas appear. We also consider how successful and self-refuting formulas relate to the Cartesian and learnable formulas, which have been discussed in connection with Fitch’s “paradox of knowability.” We show that the Cartesian formulas are exactly the formulas that are not eventually self-refuting and that not all learnable formulas are successful. In an appendix, we give syntactic characterizations of the successful and the self-refuting formulas. (shrink)

In this paper, we explore semantics for comparative epistemic modals that avoid the entailment problems shown to result from Kratzer’s (1991) semantics by Yalcin (2006, 2009, 2010). In contrast to the alternative semantics presented by Yalcin and Lassiter (2010, 2011), based on finitely additive probability measures, we introduce semantics based on qualitatively additive measures, as well as semantics based on purely qualitative orderings, including orderings on propositions derived from orderings on worlds in the tradition of Kratzer (1991). All of these (...) semantics avoid the entailment problems that result from Kratzer’s semantics. Our discussion focuses on methodological issues concerning the choice between different semantics. (shrink)

The semantic automata framework, developed originally in the 1980s, provides computational interpretations of generalized quantifiers. While recent experimental results have associated structural features of these automata with neuroanatomical demands in processing sentences with quantifiers, the theoretical framework has remained largely unexplored. In this paper, after presenting some classic results on semantic automata in a modern style, we present the first application of semantic automata to polyadic quantification, exhibiting automata for iterated quantifiers. We also discuss the role of semantic automata in (...) linguistic theory and offer new empirical predictions for sentence processing with embedded quantifiers. (shrink)

While much of semantic theorizing is based on intuitions about logical phenomena associated with linguistic constructions—phenomena such as consistency and entailment—it is rare to see axiomatic treatments of linguistic fragments. Given a fragment interpreted in some class of formally specified models, it is often possible to ask for a characterization of the reasoning patterns validated by the class of models. Axiomatizations provide such a characterization, often in a perspicuous and efficient manner. In this paper, we highlight some of the benefits (...) of providing axiomatizations for the purpose of semantic theorizing. We illustrate some of these benefits using three examples from the study of modality. (shrink)

Existing research has shown that norm violations influence causal judgments, and a number of different models have been developed to explain these effects. One such model, the necessity/sufficiency model, predicts an interac- tion pattern in people’s judgments. Specifically, it predicts that when people are judging the degree to which a particular factor is a cause, there should be an interaction between (a) the degree to which that factor violates a norm and (b) the degree to which another factor in the (...) situation violates norms. A study of moral norms (N = 1000) and norms of proper functioning (N = 3000) revealed robust evidence for the predicted interaction effect. The implications of these patterns for existing theories of causal judgments is discussed. (shrink)

This paper studies connections between two alternatives to the standard probability calculus for representing and reasoning about uncertainty: imprecise probability andcomparative probability. The goal is to identify complete logics for reasoning about uncertainty in a comparative probabilistic language whose semantics is given in terms of imprecise probability. Comparative probability operators are interpreted as quantifying over a set of probability measures. Modal and dynamic operators are added for reasoning about epistemic possibility and updating sets of probability measures.

We prove that the generalized cancellation axiom for incomplete comparative probability relations introduced by Rios Insua and Alon and Lehrer is stronger than the standard cancellation axiom for complete comparative probability relations introduced by Scott, relative to their other axioms for comparative probability in both the finite and infinite cases. This result has been suggested but not proved in the previous literature.

Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitution. A distinction therefore arises between the logic and its substitution core, the set of formulas all of whose substitution instances are valid. The classic example of a non-uniform dynamic epistemic logic is Public Announcement Logic (PAL), and a well-known open problem is to axiomatize the substitution core of PAL. In this paper we solve this problem for PAL over the class of all relational models with infinitely (...) many agents, PAL-K_omega, as well as standard extensions thereof, e.g., PAL-T_omega, PAL-S4_omega, and PAL-S5_omega. We introduce a new Uniform Public Announcement Logic (UPAL), prove completeness of a deductive system with respect to UPAL semantics, and show that this system axiomatizes the substitution core of PAL. (shrink)

The semantic automata framework, developed originally in the 1980s, provides computational interpretations of generalized quantifiers. While recent experimental results have associated structural features of these automata with neuroanatomical demands in processing sentences with quantifiers, the theoretical framework has remained largely unexplored. In this paper, after presenting some classic results on semantic automata in a modern style, we present the first application of semantic automata to polyadic quantification, exhibiting automata for iterated quantifiers. We also discuss the role of semantic automata in (...) linguistic theory and offer new empirical predictions for sentence processing with embedded quantifiers. (shrink)

The picture of information acquisition as the elimination of possibilities has proven fruitful in many domains, serving as a foundation for formal models in philosophy, linguistics, computer science, and economics. While the picture appears simple, its formalization in dynamic epistemic logic reveals subtleties: given a valid principle of information dynamics in the language of dynamic epistemic logic, substituting complex epistemic sentences for its atomic sentences may result in an invalid principle. In this article, we explore such failures of uniform substitution. (...) First, we give epistemic examples inspired by Moore, Fitch, and Williamson. Second, we answer affirmatively a question posed by van Benthem: can we effectively decide when every substitution instance of a given dynamic epistemic principle is valid? In technical terms, we prove the decidability of this schematic validity problem for public announcement logic (PAL and PAL-RC) over models for finitely many fully introspective agents, as well as models for infinitely many arbitrary agents. The proof of this result illuminates the reasons for the failure of uniform substitution. (shrink)

A well-known open problem in epistemic logic is to give a syntactic characterization of the successful formulas. Semantically, a formula is successful if and only if for any pointed model where it is true, it remains true after deleting all points where the formula was false. The classic example of a formula that is not successful in this sense is the “Moore sentence” p ∧ ¬ BOX p, read as “p is true but you do not know p.” Not only (...) is the Moore sentence unsuccessful, it is self-refuting, for it never remains true as described. We show that in logics of knowledge and belief for a single agent (extended by S5), Moorean phenomena are the source of all self-refutation; moreover, in logics for an introspective agent (extending KD45), Moorean phenomena are the source of all unsuccessfulness as well. This is a distinctive feature of such logics, for with a non-introspective agent or multiple agents, non-Moorean unsuccessful formulas appear. We also consider how successful and self-refuting formulas relate to the Cartesian and learnable formulas, which have been discussed in connection with Fitch’s “paradox of knowability.” We show that the Cartesian formulas are exactly the formulas that are not eventually self-refuting and that not all learnable formulas are successful. In an appendix, we give syntactic characterizations of the successful and the self-refuting formulas. (shrink)

Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitution. A distinction therefore arises between the logic and its substitu- tion core, the set of formulas all of whose substitution instances are valid. The classic example of a non-uniform dynamic epistemic logic is Public Announcement Logic (PAL), and a well-known open problem is to axiomatize the substitution core of PAL. In this paper we solve this problem for PAL over the class of all relational models with (...) infinitely many agents, PAL-Kω , as well as standard extensions thereof, e.g., PAL-Tω , PAL-S4ω, and PAL-S5ω. We introduce a new Uniform Public Announcement Logic (UPAL), prove completeness of a deductive system with respect to UPAL semantics, and show that this system axiomatizes the substitution core of PAL. (shrink)

Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitution. A distinction therefore arises between the logic and its substitution core, the set of formulas all of whose substitution instances are valid. The classic example of a non-uniform dynamic epistemic logic is Public Announcement Logic (PAL), and a well-known open problem is to axiomatize the substitution core of PAL. In this paper we solve this problem for PAL over the class of all relational models with infinitely (...) many agents, PAL-Kω , as well as standard extensions thereof, e.g., PAL-Tω , PAL-S4ω, and PAL-S5ω. We introduce a new Uniform Public Announcement Logic (UPAL), prove completeness of a deductive system with respect to UPAL semantics, and show that this system axiomatizes the substitution core of PAL. (shrink)

A well-known open problem in epistemic logic is to give a syntactic characterization of the successful formulas. Semantically, a formula is successful if and only if for any pointed model where it is true, it remains true after deleting all points where the formula was false. The classic example of a formula that is not successful in this sense is the “Moore sentence” p ∧ ¬ BOX p, read as “p is true but you do not know p.” Not only (...) is the Moore sentence unsuccessful, it is self-refuting, for it never remains true as described. We show that in logics of knowledge and belief for a single agent (extended by S5), Moorean phenomena are the source of all self-refutation; moreover, in logics for an introspective agent (extending KD45), Moorean phenomena are the source of all unsuccessfulness as well. This is a distinctive feature of such logics, for with a non-introspective agent or multiple agents, non-Moorean unsuccessful formulas appear. We also consider how successful and self-refuting formulas relate to the Cartesian and learnable formulas, which have been discussed in connection with Fitch’s “paradox of knowability.” We show that the Cartesian formulas are exactly the formulas that are not eventually self-refuting and that not all learnable formulas are successful. In an appendix, we give syntactic characterizations of the successful and the self-refuting formulas. (shrink)

When does it make sense to act randomly? A persuasive argument from Bayesian decision theory legitimizes randomization essentially only in tie-breaking situations. Rational behaviour in humans, non-human animals, and artificial agents, however, often seems indeterminate, even random. Moreover, rationales for randomized acts have been offered in a number of disciplines, including game theory, experimental design, and machine learning. A common way of accommodating some of these observations is by appeal to a decision-maker’s bounded computational resources. Making this suggestion both precise (...) and compelling is surprisingly difficult. Toward this end, I propose two fundamental rationales for randomization, drawing upon diverse ideas and results from the wider theory of computation. The first unifies common intuitions in favour of randomization from the aforementioned disciplines. The second introduces a deep connection between randomization and memory: access to a randomizing device is provably helpful for an agent burdened with a finite memory. Aside from fit with ordinary intuitions about rational action, the two rationales also make sense of empirical observations in the biological world. Indeed, random behaviour emerges more or less where it should, according to the proposal. (shrink)

Subjective probability plays an increasingly important role in many fields concerned with human cognition and behavior. Yet there have been significant criticisms of the idea that probabilities could actually be represented in the mind. This paper presents and elaborates a view of subjective probability as a kind of sampling propensity associated with internally represented generative models. The resulting view answers to some of the most well known criticisms of subjective probability, and is also supported by empirical work in neuroscience and (...) behavioral psychology. The repercussions of the view for how we conceive of many ordinary instances of subjective probability, and how it relates to more traditional conceptions of subjective probability, are discussed in some detail. (shrink)

A probabilistic Chomsky–Schützenberger hierarchy of grammars is introduced and studied, with the aim of understanding the expressive power of generative models. We offer characterizations of the distributions definable at each level of the hierarchy, including probabilistic regular, context-free, (linear) indexed, context-sensitive, and unrestricted grammars, each corresponding to familiar probabilistic machine classes. Special attention is given to distributions on (unary notations for) positive integers. Unlike in the classical case where the "semi-linear" languages all collapse into the regular languages, using analytic tools (...) adapted from the classical setting we show there is no collapse in the probabilistic hierarchy: more distributions become definable at each level. We also address related issues such as closure under probabilistic conditioning. (shrink)

Reasoning with quantifier expressions in natural language combines logical and arithmetical features, transcending strict divides between qualitative and quantitative. Our topic is this cooperation of styles as it occurs in common linguistic usage and its extension into the broader practice of natural language plus ‘grassroots mathematics’.We begin with a brief review of by changing the semantics of counting in natural ways. A first approach replaces cardinalities by abstract but well-motivated values of ‘mass’ or other mereological aggregating notions. A second approach (...) keeps the cardinalities but generalizes the meaning of counting to work in models that allow dependencies between variables.Finally, we return to our starting point in natural language, confronting the architecture of our formal systems with linguistic quantifier vocabulary and syntax, as well as with natural reasoning modules such as the monotonicity calculus. In addition to these encounters with formal semantics, we discuss the role of counting in semantic evaluation procedures for quantifier expressions and determine, for instance, which binary quantifiers are computable by finite ‘semantic automata’. We conclude with some general thoughts on yet further entanglements of logic and counting in formal systems, on rethinking the qualitative/quantitative divide, and on connecting our analysis to empirical findings in cognitive science. (shrink)

People often engage in “offline simulation”, considering what would happen if they performed certain actions in the future, or had performed different actions in the past. Prior research shows that these simulations are biased towards actions a person considers to be good—i.e., likely to pay off. We ask whether, and why, this bias might be adaptive. Through computational experiments we compare five agents who differ only in the way they engage in offline simulation, across a variety of different environment types. (...) Broadly speaking, our experiments reveal that simulating actions one already regards as good does in fact confer an advantage in downstream decision making, although this general pattern interacts with features of the environment in important ways. We contrast this bias with alternatives such as simulating actions whose outcomes are instead uncertain. (shrink)

Comparative research enriches semiotics and deepens its exchanges with other sciences. The work can also highlight inductive methods and socio-historically specific forms and practices, thereby helping to develop a general semiotics and a semiotics of cultures. This article compares the morphology by Vladimir Propp that inspired the Greimassian narrative schema to a small sample of narrative forms, then to Aristotle's Poetics and to a model of Hollywood films. Certain motifs and subgenres represent elementary schemas with two or three actants and (...) functions that rely on role reversal and emotions. A half dozen subgenres can be differentiated by the different affects that they aim to elicit. Greek tragedy is to evoke intense emotional states, and reveals a close interdependence between characteristics of the hero, modulations of the critical action, and the emotive effect produced. In the films, the variation of the affective intensity constitutes a key element of the narrative rhythm, and two main sequences supply opposing and complementary axiologies. A conclusion suggests the value of bringing together the semiotics of the passions, recent research on the history of the emotions, and comparative studies of how different cultures express feelings. (shrink)

External cues and internal configuration states are the likely instigators of involuntary autobiographical memories (IAMs) and déjà vu experience. Indeed, Barzykowski and Moulin discuss relevant neuroscientific evidence in this direction. A complementary line of enquiry and evidence is the study of inhibition and its role in memory retrieval, and particularly how its (dys)function may contribute to IAMs and déjà vu.

The concept of "ecological niche" is frequently employed in sociocultural anthropology, but there have been few systematic applications of it. This paper examines the utility of the concept for the analysis of social interaction and change, with special reference to complex societies. In a small agricultural valley of northern California, competition between two status groups over a scarce resource--land--has led to displacement and changing patterns of resource use. "Niche" describes the aggregate outcome of underlying processes of competition on the individual (...) level. (shrink)

Argument invention is a method that can be used to help an arguer find arguments that could be used to prove a claim he needs to defend. The aim of this paper is to show how argumentation systems recently developed in artificial intelligence can be applied to the task of argument invention. One such system called Carneades is featured. Carneades can be used to analyze arguments, evaluate arguments, to make an argument diagram, and to construct arguments from a database. Using (...) some simple examples, the paper explains how Carneades works as a system of argument invention. (shrink)

This paper presents a formalization of informal logic using the Carneades Argumentation System, a formal, computational model of argument that consists of a formal model of argument graphs and audiences. Conflicts between pro and con arguments are resolved using proof standards, such as preponderance of the evidence. CAS also formalizes argumentation schemes. Schemes can be used to check whether a given argument instantiates the types of argument deemed normatively appropriate for the type of dialogue.

In lieu of an abstract, here is a brief excerpt of the content:332 BOOK REVIEWS toral inventions (such as basic Christian communities), and the religious backgrounds of millions who help to make up the churches, Catholic and Protestant, of the United States. Providence College Providence, RI EDWARD L. CLEARY, O.P. Springs of Action: Understanding Intentional Behavior. By ALFRED R. MELE. New York and Oxford: Oxford University Press, 1992. Pp. 272 + ix. $39.95 (cloth). Alfred Mele's overarching aim in this book (...) is to offer an account of the role of intentions in the explanation of intentional action. He works within the familiar terms of causal theories of action, and is particularly indebted to Donald Davidson. In Part I, Mele borrows a set of theses from Davidson's desire/belief model of intentional action, and in the process of addressing problems associated with these theses, he progressively refines an account of action that understands an agent's reasons to have explanatory force by virtue of being among the causes of action. In Part II, Mele argues that desire/belief models are insufficient as they stand and need to be filled out by recognizing that intentions provide a crucial link between reasons and actions. The discussion begins with the vexed question of how the content of mental states can be relevant to the causal explanation of action. We constantly appeal to our desires, beliefs, plans, and so on (i.e., to various propositional, or intentional, attitudes) in explaining our behavior. But how does, say, my appetite for good wine and my belief that the house chardonnay is such a wine figure in the causal order that brings about my act of ordering a glass of it? Presumably, these intentional states supervene upon certain physical states of my body, and the latter do the causal work of producing wine-ordering behavior. However, there are good reasons to think that, with certain sorts of changes in my history and environment (viz., of the sort described in twin earth thought experiments), these physical states could be the realization of different intentional states. So can a causal theory of action actually accord my desires and beliefs any role in explaining my action? Mele argues that even if we hold (with externalists) that the agent's history and environment help to fix the content of her intentional states, we can nonetheless say that unless the agent had intended what she did, she would not have acted as she did. The behavior is intentional action by virtue of issuing (in the right way) from physical processes BOOK REVIEWS 333 that realize the agent's reasons for acting, and these processes realize these reasons only if the processes have an appropriate causal history. The result is that what we desire, believe, and intend does after all make a systematic difference in what we do. Mele makes some helpful refinements in the standard account of the causal role of desire in intentional action. It has typically been claimed that when an agent's wants compete, the "strongest" of them deter· mines the action; if an agent wants to do A more than anything else that she takes herself to be able to do, then if she acts intentionally she will do A. Mele points out that this general claim must be qualified so as to index desires to times, to accommodate both unsuccessful at· tempts and the agent's estimates of the likelihood of success, and to deal with the complex relations between desires. He explores the way in which agents are able to control the motivational strength of their desires, and he works out a definition of irresistible desire. One of the deepest challenges to the claim that action is caused by what we most desire arises in considering "motivational ties." How, on this account, is intentional action possible when we equally desire each of two incompatible alternatives? An arbitrary decision procedure can be adopted (e.g., a coin toss), but this alone does not en· hance the attractiveness of the randomly selected alternative. Here Mele introduces his thesis about intentions: viz., that intentions have an "executive quality that is not reducible to desire-strength" (p. 72), so that even when there is no preponderant motivation to do A... (shrink)

Everything about us today tells us that we live in a world which will be increasingly dominated by empirical and theoretic science. This is the world in which the Church lives and proclaims its message about Jesus Christ. It is not an alien world, for it is in this world of space and time that God has planted us. He made the universe and endowed man with gifts to investigate and understand it. Just as he made life to produce itself, (...) so he has made the universe with man as an essential constituent in it, that it may bring forth and articulate knowledge of itself. Regarded in this light the pursuit of science is one of the ways in which man exercises the dominion in the earth which he was given at his creation. That is how, for example, Francis Bacon understood the work of human science, as man's obedience to God. Science is a religious duty, while man as scientist can be spoken of as the priest of creation , whose task it is to interpret the books of nature, to understand the universe in its wonderful structures and harmonies, and to bring it all into orderly articulation, so that it fulfils its proper end as the vast theatre of glory in which the creator is worshipped and praised. Nature itself is dumb, but it is man's part to bring it to word, to be its mouth through which the whole universe gives voice to the glory and majesty of the living God. (shrink)

This paper compares the features and methods of the two leading implemented systems that offer a tool for helping a user to find or invent arguments to support or attack a designated conclusion, the Carneades Argumentation System and the IBM Watson Debater tool. The central aim is to contribute to the understanding of scholars in informal logic, rhetoric and argumentation on how these two software systems can be useful for them. One contribution of the paper is to explain to these (...) potential users how the two tools are applicable to the task of inventing arguments by using some simple illustrative examples. Another is to redefine the structure of argument invention as a procedure. (shrink)

Many tasks in statistical and causal inference can be construed as problems of entailment in a suitable formal language. We ask whether those problems are more difficult, from a computational perspective, for causal probabilistic languages than for pure probabilistic (or “associational”) languages. Despite several senses in which causal reasoning is indeed more complex—both expressively and inferentially—we show that causal entailment (or satisfiability) problems can be systematically and robustly reduced to purely probabilistic problems. Thus there is no jump in computational complexity. (...) Along the way we answer several open problems concerning the complexity of well-known probability logics, in particular demonstrating the ${\exists \mathbb {R}}$ -completeness of a polynomial probability calculus, as well as a seemingly much simpler system, the logic of comparative conditional probability. (shrink)

We present a formal, mathematical model of argument structure and evaluation, taking seriously the procedural and dialogical aspects of argumentation. The model applies proof standards to determine the acceptability of statements on an issue-by-issue basis. The model uses different types of premises (ordinary premises, assumptions and exceptions) and information about the dialectical status of statements (stated, questioned, accepted or rejected) to allow the burden of proof to be allocated to the proponent or the respondent, as appropriate, for each premise separately. (...) Our approach allows the burden of proof for a premise to be assigned to a different party than the one who has the burden of proving the conclusion of the argument, and also to change the burden of proof or applicable proof standard as the dialogue progresses from stage to stage. Useful for modeling legal dialogues, the burden of production and burden of persuasion can be handled separately, with a different responsible party and applicable proof standard for each. Carneades enables critical questions of argumentation schemes to be modeled as additional premises, using premise types to capture the varying effect on the burden of proof of different kinds of questions. (shrink)

Recent ideas about epistemic modals and indicative conditionals in formal semantics have significant overlap with ideas in modal logic and dynamic epistemic logic. The purpose of this paper is to show how greater interaction between formal semantics and dynamic epistemic logic in this area can be of mutual benefit. In one direction, we show how concepts and tools from modal logic and dynamic epistemic logic can be used to give a simple, complete axiomatization of Yalcin's [16] semantic consequence relation for (...) a language with epistemic modals and indicative conditionals. In the other direction, the formal semantics for indicative conditionals due to Kolodny and MacFarlane [9] gives rise to a new dynamic operator that is very natural from the point of view of dynamic epistemic logic, allowing succinct expression of dependence (as in dependence logic) or supervenience statements. We prove decidability for the logic with epistemic modals and Kolodny and MacFarlane's indicative conditional via a full and faithful computable translation from their logic to the modal logic K45. (shrink)

The reaction to Darwin's Origin of Species varied in many countries according to the roles played by national scientific institutions and traditions and the attitudes of religious and political groups. The contributors to this volume, including M. J. S. Hodge, David Hull, and Roberto Moreno, gathered in 1972 at an international conference on the comparative reception of Darwinism. Their essays look at early pro- and anti-Darwinism arguments, and three additional comparative essays and appendices add a larger perspective. For this paperback (...) edition, Thomas F. Glick has added a new preface commenting on recent research. (shrink)

Argument invention is a method that can be used to help an arguer find arguments that could be used to prove a claim he needs to defend. The aim of this paper is to show how argumentation systems recently developed in artificial intelligence can be applied to the task of argument invention. One such system called Carneades is featured. Carneades can be used to analyze arguments, evaluate arguments, to make an argument diagram, and to construct arguments from a database. Using (...) some simple examples, the paper explains how Carneades works as a system of argument invention. (shrink)

The Pleadings Game is a normative formalization and computational model of civil pleading, founded in Roberty Alexy''s discourse theory of legal argumentation. The consequences of arguments and counterarguments are modelled using Geffner and Pearl''s nonmonotonic logic,conditional entailment. Discourse in focussed using the concepts of issue and relevance. Conflicts between arguments can be resolved by arguing about the validity and priority of rules, at any level. The computational model is fully implemented and has been tested using examples from Article Nine of (...) the Uniform Commercial Code. (shrink)

This paper presents a formalization of informal logic using the Carneades Argumentation System, a formal, computational model of argument that consists of a formal model of argument graphs and audiences. Conflicts between pro and con arguments are resolved using proof standards, such as preponderance of the evidence. Carneades also formalizes argumentation schemes. Schemes can be used to check whether a given argument instantiates the types of argument deemed normatively appropriate for the type of dialogue.

This paper shows how the critical questions matching an argumentation scheme can be mod-eled in the Carneades argumentation system as three kinds of premises. Ordinary premises hold only if they are supported by sufficient arguments. Assumptions hold, by default, until they have been questioned. With exceptions the negation holds, by default, until the exception has been supported by sufficient arguments. By “sufficient arguments”, we mean arguments sufficient to satisfy the applicable proof standard.