Modern logic is about information flow and communication far beyond its traditional agenda of inference and meaning. This makes it a player at a central academic interface between many disciplines, where normative and descriptive stances, often thought to be at odds, meet in creating new practices which also affect reality. This same theatre is where philosophy in general would thrive, if it so wished.

Modern logic is about information flow and communication far beyond its traditional agenda of inference and meaning. This makes it a player at a central academic interface between many disciplines, where normative and descriptive stances, often thought to be at odds, meet in creating new practices which also affect reality. This same theatre is where philosophy in general would thrive, if it so wished.

The Joint International Conference on Logic Programming, sponsored by the Association for Logic Programming, is a major forum for presentations of research, applications, and implementations in this important area of computer science. Logic programming is one of the most promising steps toward declarative programming and forms the theoretical basis of the programming language Prolog and its various extensions. Logic programming is also fundamental to work in artificial intelligence, where it has been used for nonmonotonic and (...) commonsense reasoning, expert systems implementation, deductive databases, and applications such as computer-aided manufacturing. Krzysztof R. Apt is project leader at the Centre for Mathematics and Computer Science in Amsterdam and part-time Professor in Computer Science at the University of Amsterdam. Topics covered: Theory Foundations. Programming Languages. Implementation. Programming Methodologies and Tools. Applications. Deductive Databases. Artificial Intelligence. Parallelism. (shrink)

The First International Workshop brings together researchers from the theoretical ends of the logic programming and artificial intelligence communities to discuss their mutual interests. Logic programming deals with the use of models of mathematical logic as a way of programming computers, where theoretical AI deals with abstract issues in modeling and representing human knowledge and beliefs. One common ground is nonmonotonic reasoning, a family of logics that includes room for the kinds of variations that can be (...) found in human reasoning. Topics covered: Stable Semantics. Default Logic. AutoEpistemic Logic. Truth Maintenance Systems. Implementation Issues. Diagnosis. Applications. Inheritance Reasoning. Logics of Belief. Inconsistency and Non-Monotonicity. (shrink)

Recent years have seen a surge of attention to the problem of logical pluralism; most of which has been a reaction to Beall and Restall’s account of logical pluralism as the existence of more than one equally correct semantic relation of logical consequence. The underlying thesis is that the indeterminacy of the notion of validity goes beyond what the inductive-deductive distinction can precisify. The notion of deductive validity itself is indeterminate as well and this indeterminacy has its roots in the (...) indeterminacy of the more fundamental notion of case. Cases are what make the premisses and the conclusion of an argument true; the most notable example being Tarskian models for classical logic. Deductive validity is the preservation of truth across all cases. This paper argues that unless this account of logical pluralism is supplemented with an argument in favor of the equal legitimacy of the purported cases it becomes merely a semi-controversial exposition of how different logics can be generated. (shrink)

hese notes don’t reach any conclusions. Their purpose is to point to issues one needs to think through seriously when thinking about logic teaching. They indicate some of the relevant literature where some of these issues are addressed, but they also raise points that seem to have been overlooked. They aim to promote informed discussion. That indeed was their origin: they are descended from an internal discussion document prepared a few years ago when the then Department of Philosophy (...) at the University of Edinburgh was reviewing its logic teaching. (shrink)

Epistemic logic begins with the recognition that our everyday talk about knowing and believing has some systematic features that we can track and re‡ect upon. Epistemic logicians have studied and extended these glints of systematic structure in fascinating and important ways since the early 1960s. However, for one reason or another, mainstream epistemologists have shown little interest. It is striking to contrast the marginal role of epistemic logic in contemporary epistemology with the centrality of modal logic for (...) metaphysicians. This article is intended to help in correcting this oversight by presenting some important developments in epistemic logic and suggesting ways to understand their applicability to traditional epistemological problems. Obviously, by itself, tweaking the formal apparatus of epistemic logic does not solve traditional epistemological problems. Epistemic logic can help us to navigate through problems in a systematic fashion by unpacking the logic of the problematic concepts, it can also lead us to recognize problems that we had not anticipated. This is basically analogous to the role that modal logic has played in contemporary metaphysics. (shrink)

In this paper, we make distinctions between Classical Logic (where the propositions are 100% true, or 100 false) and the Neutrosophic Logic (where one deals with partially true, partially indeterminate and partially false propositions) in order to respond to K. Georgiev’s criticism [1]. We recall that if an axiom is true in a classical logic system, it is not necessarily that the axiom be valid in a modern (fuzzy, intuitionistic fuzzy, neutrosophic etc.) logic system.

I read Stefan Collini’s What are Universities For? last week with very mixed feelings. In the past, I’ve much admired his polemical essays on the REF, “impact”, the Browne Report, etc. in the London Review of Books and elsewhere: they speak to my heart. If you don’t know those essays, you can get some of their flavour from his latest article in the Guardian yesterday. But I found the book a disappointment. Perhaps the trouble is that Collini is too decent, (...) too high-minded, has too unrealistically exalted a view about what actually happens in universities which is too coloured by attitudes appropriate to the traditional humanities. And he is optimistic to the point of fantasy if he thinks that people are so susceptible to “the romance of ideas and the power of beauty” that they will want, or can be brought to want, lots and lots of universities in order to promote the ideas (as if they would suppose that the task of “conserving, understanding, extending and handing on to subsequent generations the intellectual, scientific, and artistic heritage of mankind” was clearly ill-served when there were only forty universities in England, as opposed to a hundred and whatever). (shrink)

If to be is to be the value of a bound variable, then the acknowledgment and denial of the existence of chairs amounts to a serious disagreement about the range of a quantifier. However, by resorting to the intrinsic hierarchical structure of hi-world semantics, we find that the varying of domains from worlds to worlds can actually be accommodated within a unified framework. With the introduction of a universal domain D of hi-individuals and an existence predicate E that serves as (...) a realization operator, a new semantics for quantified modal logic is proposed. It allows individual variables to range over individuals in different levels of a hi-world, and is indifferent to the ontological debate about the existence of chairs. (shrink)

We investigate the research programme of dynamic doxastic logic (DDL) and analyze its underlying methodology. The Ramsey test for conditionals is used to characterize the logical and philosophical differences between two paradigmatic systems, AGM and KGM, which we develop and compare axiomatically and semantically. The importance of Gärdenfors’s impossibility result on the Ramsey test is highlighted by a comparison with Arrow’s impossibility result on social choice. We end with an outlook on the prospects and the future of DDL.

ABSTRACT We investigate a logic PFD, as introduced in [FA]. In our notation, this logic is enriched with operators P> r(r € [0,1]) where the intended meaning of P> r φ is “the probability of φ (at a given world) is strictly greater than r”. We also adopt the semantics of [FA]: a class of “F-restricted probabilistic kripkean models”. We give a completeness proof that essentially differs from that in [FA]: our “peremptory lemma” (a lemma in PFD (...) rather than about it) facilitates the construction of a canonical model for PFD considerably. We show that this construction can be carried out using only finitary means, and also give a filtration-technique for the intended models. We then define an alternative (in some sense more natural) semantics for the logic, and show some of its properties. Finally, we prove decidability of the logic. (shrink)

Not all probability ascriptions that appear in scientific theories describe chances. There is a question about whether probability ascriptions in non-fundamental sciences, such as those found in evolutionary biology and statistical mechanics, describe chances in deterministic worlds and about whether there could be any chances in deterministic worlds. Recent debate over whether chance is compatible with determinism has unearthed two strategies for arguing about whether a probability ascription describes chance—that is, to speak metaphorically, two different strategies for figuring out (...) class='Hi'>where the chances are: find the chances by focusing on chance’s explanatory role or find the chances by focusing on chance’s predictive role. These two strategies tend to yield conflicting results about where the chances are, and debate over which strategy is appropriate tends to end in stalemate. After discussing these two strategies, I consider a new view of chance’s explanatory role. I argue that one theoretical advantage of this new view is that allows us to make progress on the question of where the chances are by providing a principled way of determining which probability ascriptions describe chances. From the vantage of this new view, the correct application of both strategies involves figuring out where the chances are by figuring out where the probabilistic scientific explanations are and what those explanations are like. (shrink)

Theory of Mind (ToM), the cognitive capacity to attribute internal mental states to oneself and others, is a crucial component of social skills. Its formal study has become important, witness recent research on reasoning and information update by intelligent agents, and some proposals for its formal modelling have put forward settings based on Epistemic Logic (EL). Still, due to intrinsic idealisations, it is questionable whether EL can be used to model the high-order cognition of ‘real’ agents. This manuscript proposes (...) a framework that takes visibility, memory, perspective and communication as the main factors underpinning mental attributions. This is more in-line with findings in cognitive science and allows us to model well-known False-Belief Tasks that are typically used in testing people's ToM. We discuss some of the framework's technical features, arguing why it does justice to empirical observations. (shrink)

Bayesian prior probabilities have an important place in probabilistic and statistical methods. In spite of this fact, the analysis of where these priors come from and how they are formed has received little attention. It is reasonable to excuse the lack, in the foundational literature, of detailed psychological theory of what are the mechanisms by which prior probabilities are formed. But it is less excusable that there is an almost total absence of a detailed discussion of the highly differentiating (...) nature of past experience in forming a prior. The focus here is on what kind of account, even if necessarily schematic, can be given about the psychological mechanisms back of the formation of Bayesian priors. The last section examines a detailed experiment relevant to how priors are learned. (shrink)

The book aims to formalise tableau methods for the logics of propositions and names. The methods described are based on Set Theory. The tableau rule was reduced to an ordered n-tuple of sets of expressions where the first element is a set of premises, and the following elements are its supersets.

Cathoristic logic is a multi-modal logic where negation is replaced by a novel operator allowing the expression of incompatible sentences. We present the syntax and semantics of the logic including complete proof rules, and establish a number of results such as compactness, a semantic characterisa- tion of elementary equivalence, the existence of a quadratic-time decision pro- cedure, and Brandom’s incompatibility semantics property. We demonstrate the usefulness of the logic as a language for knowledge representation.

Bayesian epistemology has close connections to inductive reasoning, accepting the view that inductive inferences should be analyzed in terms of epistemic probabilities. An important precept of Bayesian epistemology is the dynamics of belief change, with change in belief resulting from updating procedures based on new evidence. The inductive relations between evidence E and hypotheses or theories H are essential, particularly the notions of plausibility, confirmation, and acceptability, which are critical but subject to several difficulties. As a non-deductive process, Bayesian reasoning (...) cannot itself be subjected to strict deductive logic, but it can take advantage of an enabling logical environment. The present paper proposes that paraconsistent and paracomplete logics can be helpful for some questions of Bayesian epistemology, even to the point of being relevant in developing a legitimate paraconsistent Bayesian epistemology. By developing a novel probability theory based on the Logic of Evidence and Truth ( $${LET}_{F}$$ ), a logic that deals with evidence for or against a judgment, including contradictory or missing evidence, we allow for the possibility of quantifying the degree of evidence attributed to a proposition through novel probability measures. We illustrate, through examples, some ways to address challenging problems in the area by using paraconsistent and paracomplete paradigms. This topic is of significant interest not only in the philosophy of science but also in Artificial Intelligence and other emerging trends such as probabilistic networks and related models (see Haenni et al. Probabilistic logics and probabilistic networks, volume 350, Springer, Berlin, 2010). (shrink)

Go back to An-fang, the Peace Square at An-Fang, the Beginning Place at An-Fang, where all things start (… ) An-Fang was near a city, the only living city with a pre-atomic name (… ) The headquarters of the People Programmer was at An-Fang, and there the mistake happened: A ruby trembled. Two tourmaline nets failed to rectify the laser beam. A diamond noted the error. Both the error and the correction went into the general computer. Cordwainer SmithThe Dead (...) Lady of Clown Town, 1964. (shrink)

We introduce the logics GLP Λ, a generalization of Japaridze’s polymodal provability logic GLP ω where Λ is any linearly ordered set representing a hierarchy of provability operators of increasing strength. We shall provide a reduction of these logics to GLP ω yielding among other things a finitary proof of the normal form theorem for the variable-free fragment of GLP Λ and the decidability of GLP Λ for recursive orderings Λ. Further, we give a restricted axiomatization of the (...) variable-free fragment of GLP Λ. (shrink)

This chapter contains sections titled: Way 1: Fictional Truth Way 2: Other Dimensions Interlude: Could There have been a Twilight Zone? Way 3: Real Non‐Existence Way 4: Modal Realism Way 5: Abstract Fictional Realism Conclusion Notes.

A major question for the relevant logics has been, “Under what conditions is Ackermann's ruleγ from -A ∨B andA to inferB, admissible for one of these logics?” For a large number of logics and theories, the question has led to an affirmative answer to theγ problem itself, so that such an answer has almost come to be expected for relevant logics worth taking seriously. We exhibit here, however, another large and interesting class of logics-roughly, the Boolean extensions of theW — (...) free relevant logics (and, precisely, the well-behaved subsystems of the 4-valued logicBN4) — for which γ fails. (shrink)

An introductory logic textbook where the central concept is not deduction but search and logical form. (Deduction - logical consequence - drops out as a special case. TIt is meant for a class-based rather than a lecture-based course, and for students with general interests.

Internalization is a key property of justification logics. It states that justification logics internalize their own notion of proof which is essential for the proof of the realization theorem. The aim of this note is to show how to make use of internalization to track where an agent’s knowledge comes from and how to apply this to the problem of data privacy.

We present a sound and complete Fitch-style natural deduction system for an S5 modal logic containing an actuality operator, a diagonal necessity operator, and a diagonal possibility operator. The logic is two-dimensional, where we evaluate sentences with respect to both an actual world (first dimension) and a world of evaluation (second dimension). The diagonal necessity operator behaves as a quantifier over every point on the diagonal between actual worlds and worlds of evaluation, while the diagonal possibility quantifies (...) over some point on the diagonal. Thus, they are just like the epistemic operators for apriority and its dual. We take this extension of Fitch’s familiar derivation system to be a very natural one, since the new rules and labeled lines hereby introduced preserve the structure of Fitch’s own rules for the modal case. (shrink)

We present a sound and complete Fitch-style natural deduction system for an S5 modal logic containing an actuality operator, a diagonal necessity operator, and a diagonal possibility operator. The logic is two-dimensional, where we evaluate sentences with respect to both an actual world (first dimension) and a world of evaluation (second dimension). The diagonal necessity operator behaves as a quantifier over every point on the diagonal between actual worlds and worlds of evaluation, while the diagonal possibility quantifies (...) over some point on the diagonal. Thus, they are just like the epistemic operators for apriority and its dual. We take this extension of Fitch’s familiar derivation system to be a very natural one, since the new rules and labeled lines hereby introduced preserve the structure of Fitch’s own rules for the modal case. (shrink)

For the most part, attention occurs as a theme adjacent to much more topical and innovatingly operating acts: first, the intentional act, which represents a destitution of the abstract opposition between subject and object and which paves the way for a detailed analysis of our perceptive horizontal subjective life; second, the reductive act, specified in a psycho-phenomenological sense as a reflective conversion of the way I am looking at things; third, the genetic method understood as a genealogy of logic (...) based on our experiential affective pre-discursive world-life. In this respect, here are some of the leading questions of my investigation: What are the differences and the proximities between these methods and attentional activity? Why is the latter not put to the fore as a method? To what extent is this secondary part played by attention linked to the constitution of phenomenology as opposed to psychology (for which attention is a central theme), and what does it mean for the impossibility of phenomenology to freeing itself completely from psychology? (shrink)

Most commentators have underplayed the philosophical importance of Wittgenstein's multifarious remarks on music, which are scattered throughout his Nachlass. In this dissertation I spell out the extent and depth of Wittgenstein's engagement with certain problems that are regarded today as central to the field of the aesthetics of music, such as musical temporality, expression and understanding. By considering musical expression in its relation to aspect-perception, I argue that Wittgenstein understands music in terms of a highly evolved, vertically complex physiognomic language-game, (...) in which fine shades of behavior are logically (semantically) connected with the musical experiences themselves. A musical passage conjoins the multifarious language games that are presupposed in it and the emerging gesture that ultimately insinuates itself into our life. Wittgenstein conceives music as a mode of expression, a path leading from the world of our thoughts and feelings, which in itself is not yet music, toward a gesture which is no longer music, but which belongs to the world of thoughts and feelings. A melody can be located at this crossroads of music, language and the world, and is understood in reciprocal action with language. Musical gesture insinuates itself into our life, for, like a human face, it speaks of and reflects our "knowledge of mankind," and it is ultimately understood only against the background of "the bustle of life," as Wittgenstein calls it. I also argue that Wittgenstein's discussion of musical understanding suggests an important model, albeit not an exclusive one, for understanding language. The musicality of language points first and foremost at the way we use words in the vertically complex language game of expression, and at the intransitive understanding that goes with it. Throughout the dissertation I address a number of unique topics that have rarely, if ever, been investigated in this context. These include inter alia Wittgenstein's 1912-1913 experiments on the perception of rhythm, Oswald Spengler's influence on Wittgenstein's remarks on music, Wittgenstein's reaction to Heinrich Schenker's view of music, and the complex, elusive relation between Wittgenstein's later philosophical views and Arnold Schoenberg's dodecaphonic music. (shrink)

A signed -equation is an expression of the form t t or t t, where t and t are -terms (for some ranked set ). We characterize those classes of -algebras which are models of a set of signed -equations. Further we consider the problem of finding a complete deductive system analogous to equational logic for the logical consequence operation restricted to signed equations.

Frederick Grinnell’s “Everyday Practice of Science” is an ambitious attempt to survey the methodological issues facing practicing scientists. His examples and anecdotes are mainly drawn from his own field of biochemistry, which he argues is representative of the scientific method in general because, quoting Nobel Laureate Sir Peter Medawar, “Biologists work very close to the frontier between bewilderment and understanding.”(p.4) Grinnell’s goal is to explore the ambiguity and messiness of actual scientific practice, but not with an eye to undermine its (...) credibility. Rather, he tries to show how the day-to-day practice of science functions to generate reliable hypotheses from the complexity of reality. (shrink)

François Laruelle's writing on Non-Photography is examined from its ontological condition to its desired form of a unity derived from the work of Kant, discussing precisely how the logic of transcendence and the ontology of immanence central to Laruelle's theory impact on how the photographic image is incontrovertibly involved with Kant's paradox of appearance and reality. In a context of burgeoning technoscience, which lays bare the meaning of Non-Photography for the seemingly impossible reversion to actual photography, the article goes (...) on to consider Photo-Fiction in the context of the Real of science now yoked to an economy of technical models. But by foreclosing the Kantian Real by fractal‐virtual ratio, does not this science reify the Real of Identity and displace real photography with a photography in the Real? The article thus questions how Laruelle's' thesis hangs together in terms of its cause and the contingency of effect that infuses Laruelle's radical aesthetic. (shrink)

The authors ground their reflections on gender and the complex realities of the second Palestinian intifada against Israeli occupation in the political processes unleashed by the signing of the Israeli–Palestinian rule, noting that the profound inequalities between Israel and Palestine during the interim period produced inequalities among Palestinians. The apartheid logic of the Oslo period – made explicit in Israel's policies of separation, seige and confinement of the Palestinian population during the intifada and before it – is shown to (...) shape the forms, sites and levels of resistance which are highly restricted by gender and age. In addition, the authors argue that the Palestinian Authority and leadership have solved the contradictions and crisis of Palestinian nationalism in this period through a form of rule that the authors term ‘authoritarian populism’, that tends to disallow democractic politics and participation. The seeming absence of women and civil society from the highly unequal and violent confrontations is contrasted with the first Palestinian intifada (1987–91), that occurred in a context of more than a decade of democratic activism and the growth of mass-based organizations, including the Palestinian women's movement. The authors explore three linked crises in gender roles emerging from the conditions of the second intifada: a crisis in masculinity, a crisis in paternity and a crisis in maternity. (shrink)

Recently, whether or not moral enhancement is permissible has been a hot issue in a new academic field of neuroethics. Several scholars have proposed moral enhancement as a reliable solution to the serious moral evils that humans face. They believe that we should pursue and employ biomedical means to morally enhance human beings. They suggest that there are in principle no philosophical or moral objections to the use of biomedical means of moral enhancement and that the current moral predicament of (...) humankind is so serious that it is imperative that scientific research explore every possibility of developing effective means of moral enhancement, as a complement of traditional means. The purpose of this article was to analyze the errors of such a suggestion in a critical manner. In a viewpoint of ethics, moral enhancement commits three important errors such as compulsion, reductionism, and methodological individualism. In a viewpoint of pedagogy, it is not based on the logic of education but that of simple designing. Furthermore, moral enhancement does deny the right to negotiate children's moral identities. Therefore, it is not persuasive that moral enhancement for all the people should be done in obligatory or compulsory ways. (shrink)

According to certain normative theories in epistemology, rationality requires us to be logically omniscient. Yet this prescription clashes with our ordinary judgments of rationality. How should we resolve this tension? In this paper, I focus particularly on the logical omniscience requirement in Bayesian epistemology. Building on a key insight by Hacking :311–325, 1967), I develop a version of Bayesianism that permits logical ignorance. This includes: an account of the synchronic norms that govern a logically ignorant individual at any given time; (...) an account of how we reduce our logical ignorance by learning logical facts and how we should update our credences in response to such evidence; and an account of when logical ignorance is irrational and when it isn’t. At the end, I explain why the requirement of logical omniscience remains true of ideal agents with no computational, processing, or storage limitations. (shrink)

This paper introduces deontic logic based on inquisitive semantics. A semantics for action formulas is introduced where each action formula is associated with a set of alternatives. Deontic operators are then interpreted as quantifying over all alternatives associated with the action formulas within their scope. It is shown how this construction provides solutions to problems related to free choice permissions and obligations, including issues concerning Hurford disjunctions. The main technical result is a complete axiomatization of the logic.

Natural languages are riddled with context-sensitivity. One and the same string of words can express many different meanings on occasion of use, and yet we understand one another effortlessly, on the fly. How do we do so? What fixes the meaning of context-sensitive expressions, and how are we able to recover the meaning so effortlessly? -/- This book offers a novel response: we can do so because we draw on a broad array of subtle linguistic conventions that determine the interpretation (...) of context-sensitive items. Contrary to the dominant tradition, which maintains that the meaning of context-sensitive language is underspecified by grammar and that interpretation relies on non-linguistic cues and speakers' intentions, this book argues that meaning is determined entirely by discourse conventions, rules of language that have largely been missed and the effects of which have been mistaken for extra-linguistic effects of an utterance situation on meaning. The linguistic account of context developed here sheds new light on the nature of linguistic content and the interaction between content and context. At the same time, it provides a novel model of context that should constrain and help evaluate debates across many subfields of philosophy where appeal to context has been common, often leading to surprising conclusions such as epistemology, ethics, value theory, metaphysics, metaethics, and logic. (shrink)

Discussions about dispositional and categorical properties have become commonplace in metaphysics. Unfortunately, dispositionality and categoricity are disputed notions: usual characterizations are piecemeal and not widely applicable, thus threatening to make agreements and disagreements on the matter merely verbal—and also making it arduous to map a logical space of positions about dispositional and categorical properties in which all parties can comfortably fit. This paper offers a prescription for this important difficulty, or at least an inkling thereof. This will be achieved by (...) comparing pairs of positions and exploring their background metaphysics to discover where alleged agreements and disagreements concerning dispositionality and categoricity really lie; more specifically, the Pure Powers view and the Powerful Qualities view will be under scrutiny. Over this background, the prescription functions by isolating a successful identity-based characterization of categoricity, while abandoning the correspondent identity-based characterization of dispositionality. On the contrary, according to this prescription a property is dispositional if and only if it is solely in virtue of possessing that property that its bearer is assigned a certain dispositional profile. A crucial consequence of this prescription is that, while supporters of the Pure Powers view often characterize their position as an essentialist one, the dispositionality of properties needn’t always be a matter of essence. (shrink)

Dynamic Topological Logic () is a combination of , under its topological interpretation, and the temporal logic interpreted over the natural numbers. is used to reason about properties of dynamical systems based on topological spaces. Semantics are given by dynamic topological models, which are tuples , where is a topological space, f a function on X and V a truth valuation assigning subsets of X to propositional variables. Our main result is that the set of valid formulas (...) of over spaces with continuous functions is recursively enumerable. We show this by defining alternative semantics for . Under standard semantics, is not complete for Kripke frames. However, we introduce the notion of a non-deterministic quasimodel, where the function f is replaced by a binary relation g assigning to each world multiple temporal successors. We place restrictions on the successors so that the logic remains unchanged; under these alternative semantics, becomes Kripke-complete. We then apply model-search techniques to enumerate the set of all valid formulas. (shrink)

Abstract The purpose of this paper is twofold: (i) we will argue that formal semantics might have faltered due to its failure in distinguishing between two fundamentally very different types of concepts, namely ontological concepts, that should be types in a strongly-typed ontology, and logical concepts, that are predicates corresponding to properties of, and relations between, objects of various ontological types; and (ii) we show that accounting for these differences amounts to a new formal semantics; one that integrates lexical and (...) compositional semantics in one coherent framework and one where formal semantics is embedded with a strongly typed ontology; an ontology that reflects our commonsense knowledge of the world and the way we talk about it in ordinary language. We will show how in such a framework a number of challenges in the semantics of natural language are adequately and systematically treated. (shrink)

We study a new formal logic LD introduced by Prof. Grzegorczyk. The logic is based on so-called descriptive equivalence, corresponding to the idea of shared meaning rather than shared truth value. We construct a semantics for LD based on a new type of algebras and prove its soundness and completeness. We further show several examples of classical laws that hold for LD as well as laws that fail. Finally, we list a number of open problems. -/- .

Let PLω be the provability logic of IΔ0 + ω1. We prove some containments of the form L ⊆ PLω < Th(C) where L is the provability logic of PA and Th(C) is a suitable class of Kripke frames.