Wednesday, August 1, 2018

Review of Compositional Semantics, by Pauline Jacobson

Review of Compositional Semantics, by Pauline Jacobson

Jacobson’s textbook book falls into the category of introductory semantics textbooks for advanced undergraduates and beginning grads. It distinguishes itself from the competitors by emphasizing two leading ideas: direct compositionality and variable-free semantics. There is also an emphasis throughout the textbook on issues in pronominal reference. As with the other introductory semantics textbooks on the market, I would recommend that students are familiar with basic propositional and predicate logic before taking a course based on this book. Also, since the book makes regular comparisons between the direct compositionality approach and structure based approaches, an introductory course in syntax would be useful.
Direct compositionality is defined as follows (pg. 43): “The semantics works in tandem with the syntax: each syntactic rule which predicts the existence of some well-formed expression (as output) is paired with a semantic rule which gives the meaning of the output expression in terms of the meaning(s) of the input expressions.” This leading idea determines how she formulates the rules of semantic interpretation. She devises a system where triples of the form <[sound], syntactic category, [[meaning]]> are manipulated by various unary (operating on one triple) and combinatory rules (operating on two triples to combine them into one).
Crucially, in this framework, no syntactic structures of the form familiar from Principles and Parameters syntax or Minimalist syntax are formed. A direct consequence of this approach, which Jacobson does not comment upon, is that it is actually impossible to formulate movement in her framework. In order to formulate movement, one must form a syntactic structure from which movement takes place. For example, in the relative clause construction the man who I saw, in order to move who to Spec CP, the TP [I saw who] must be formed first with the wh-phrase who in-situ. But in Jacobson’s framework, no such pre-movement structure is formed. Rather, every time two triples are put together (e.g., the triple for I and the triple for saw), a third triple is formed and the resulting triple contains no syntactic structure. In this sense, Jacobson’s framework is the most derivational framework of syntax possible. There literally are no syntactic structures (other than the syntactic category labels, which happen to contain quite a bit of syntactic information in categorical grammar). Jacobson has done us a valuable service in formulating her derivational approach so carefully.
It is interesting to compare minimalist syntax with Jacobson’s framework. One way to look at minimalist syntax is as a kind of deviation from Jacobson’s ideal that is consistent with movement. Minimalist syntax is based on the operation Merge(X,Y) which forms syntactic objects, but these syntactic objects are not interpreted right away. At the phase level (e.g., vP or CP), the complement of the phase head is sent to the interfaces. The edge of the phase (head and specifier of the phase) is not sent to the interfaces. This formalism allows cyclic spell-out/interpretation, while at the same time allowing constituents to move to the edge of the phase. Minimalist syntax is derivational in the sense that there is a sequence of structures, each one related to the previous one by some syntactic operation (e.g., Merge). But minimalist syntax is also representational, since syntactic structures are formed which are sent to the interfaces.
Comparing direct compositionality with minimalist syntax and Principles and Parameters syntax gives a kind of cline of derivationality, with direct compositionality being the most derivational. An interesting question for further research is what other kinds of deviations from Jacobson’s framework could be imagined that would allow for movement. Are phases in the sense of present day minimalism really necessary? Instead of phases, one could imagine an approach where after forming {X,Y} by Merge, internal Merge forms{Y, {X,Y}}, and then {X,Y} is interpreted. How to formalize such an approach is beyond the scope of this review. Could Jacobson’s approach be modified to allow some structure building in addition to simultaneous interpretation so that the triples are <[sound], syntactic structure, [[meaning]]>? If so, then movement could possibly take place from the syntactic structure. Serious consideration of Jacobson’s approach and comparison to current minimalist syntax (by both syntacticians and semanticists) would be a valuable undertaking.
Variable-free semantics is defined as an approach which makes no use of indices, assignments, variables (pg., 286), or traces (pg. 229). It is important to specify here that the indices, assignments and variables being referred to are those in the syntax or the syntax-semantics interface. So for example, it is not necessary to co-index expressions in a variable-free framework. Also, the Tarskian assignment functions that are used in other frameworks (and basic logic textbooks) to assign values to variables are not necessary either. However, many of the semantic values that are calculated for various expressions do have variables in them. Take for example, the semantic value of every pig: lP["x[pig’(x) à P(x)]] (pg. 163). Even though this semantic value does contain a variable, that variable is in no way present in either the syntax or syntax-semantic interface. Rather, the semantic value of every pig names a model-theoretic object, which is a function which takes characteristic functions of sets and produce a truth value. The variable used in the semantic value is just a convenient way to help name the relevant model-theoretic object.
To get a taste for how the variable-free approach works, consider the free variable in a sentence like that in (1):

(1)       He lost.

            The basic idea is that a pronoun denotes an identity function of type <e,e>. But since lost has the semantic type <e,t>, it cannot combine with the pronoun as is, and it must be shifted to another type <<e,e>,<e,t>> (by g-sup). The shifted lost combines with the pronoun, producing the expression he lost which denotes a function from individuals to truth values. In fact, any expression containing a free variable such as (1) has type <e,X> where X is the type of the expression without the free variable. In this way, the free variable is percolated up the structure. At no point is the notion of index or assignment function made use of.
What are the advantages of a variable-free approach? While direct compositionality seems to be intuitively desirable (putting aside the issue of movement), the issue of variable-free semantics is more slippery. It seems that the variable and variable-free approach have the same empirical range, while they each involve complications of a different nature. The variable-free approach involves various type shifting rules (g-sl, argslot-l, g-sup, z) that are not needed in the variable approach. But then the variable approach needs assignment functions and a rule of lambda abstraction (pg. 218), which are not needed by the variable-free approach.
There are a few pages in the book where some general comments comparing the two approaches are made (pgs. 276 on overall simplicity, 294 on free pronouns, 368-369 on the functional meaning for questions, 374 on paycheck pronouns and 382 on the paycheck generalization), but I feel that a longer summary (perhaps a whole section) pulling these various observations together and comparing the two approaches in one place would have been useful, and would have helped me clarify in my mind what the issues were. As it stands, the variable-free approach comes across as a formal alternative, and one is left without a clear idea of why one should choose one approach over the other.
            Jacobson is careful to note in the foreword that the direct compositional approach is not crucially tied to variable-free semantics. She notes that it is possible to formulate an approach which is directly compositional, but makes use of variables (pg. xviii). However, she decided to leave out such a presentation because: “… to develop three approaches to a single domain was bound to be just too much for an introductory book.” I agree it would have made the volume too big to include all possible combinations of +/- directly compositional, +/- variable-free.
            Overall, I felt that the volume could have been made more user friendly. Even the easy (non-starred) exercises seemed challenging, and there was a paucity of easier exercises emphasizing computational skills (instead of problem solving). In the ideal world, there would also have been some worked out exercises at the end of the volume or online in order to facilitate self-study. Also, I would have liked to see more semantic calculations presented in their entirety. These calculations really helped me understand what Jacobson was trying to convey in the book. The book claims that there is an associated website, which is listed with two different URLs (see pages xix and 276), neither one of which works. That is unfortunate since one is promised “a fully Direct Compositional account using variables” (pg. 276) which I would have liked to read about.
            An area where the book excels, in my opinion, is in the presentation of material on anaphora. The introduction ends with an optional section on a puzzle in pronominal reference (the i-within-i constraint). This puzzle sets the tone for the volume. Right away, one sees that there will be an emphasis on puzzling but interesting linguistic phenomena. In fact, there are two full chapters dedicated to pronouns and anaphora (chapters 15 and 17). On the other hand, I did not feel that the chapter on focus (chapter 18) added much to the volume in terms of understanding the mechanisms of direct compositionality and variable-free semantics. The information is available in introductory articles in other locations.
I give a list of errors I found while reading the book. I did not read particularly carefully, since I was trying to understand the content. I suspect there are a much larger number of errors. These errors may pose problems for the reader in understanding the text (especially in the technical semantic derivations).

Pg. 16, line under (12), (11) à (13)
Pg. 18, two lines above (19), (17) à (16)
Pg. 18, in gray box, (7) à (8), (8) à (9)
Pg. 20, five lines above grey box, “thus” should be capitalized.
Pg. 23, middle of first full paragraph, remove “and” from {m,c,g,and,p}
Pg. 29, paragraph under (2), four lines from bottom, “values” à “values is”
Pg. 46, (2), “dive” à “diving”
Pg. 59, seventh line under (8), “call ed” à “called”
Pg. 64, (13), w should be superscript in first line
Pg. 65, grey box, “is-howling” à “howl”, “is-coughing” à “cough”
Pg. 72, first line above (10), (7) à (6)
Pg. 81, second line “single” à “a single”
Pg. 83, grey box, third line of FR-3, NP à VP
Pg. 105, third line from bottom, should be F with subscript A/B
Pg. 125, second line of (11), should be N/N with an R subscript, same correction for N/N fourth line from bottom of page
Pg. 139, third line of last paragraph, “assigned to i” should be “assigned to xi”
Pg. 141, fourth line under (2), should be “f was fed only by f”          
Pg. 147, first line of section 9.2.2, “interest is” –> “interest”
Pg. 152, second line under (21), “killed” à “chased”
Pg. 154, example (23), type of B should be <a,t>
Pg. 176, (35), second line, after N, should be wolf’
Line for “every cat”, S should be a subscript on T,
Line for “every cat and no wolf” L should be a subscript twice
Next line, S should be a subscript in T,
Next line, S should be a subscript on cat’
Next line, S should be a subscript on cat’
Pg., 183, fourth line under (4), “is the” à “is in the”
Pg. 184, three lines under (5), “non-empty” à “empty”
Pg. 187, grey box, wording of “from the two” (some kind of error in wording)
Pg. 193, last line, “hypothesis processing” à “processing hypothesis”
Pg. 194, first paragraph, third line from bottom, “looks” à “look”
Pg. 200, (4), “chased and caught Br’er Rabbit” line, L should be subscript,
Next line, “chase’(x)(y)” should be “chase’(r)(y)”
Second line from bottom, same problem
Pg. 203, last line, C should be replaced with join symbol
Pg. 221, second to last line, g should be g0f (composed function),
and “a2 to c1” should be “a2 to c2”.
Pg. 231, fourth line above grey box, <e,t> à <s,t>
Pg. 256, (6), there should be three ] brackets at end
Pg. 261, two lines below grey box, there are no three-place verbs in (4)
Pg. 270, last line, “is that” à “that is”
Pg. 288, first line, <e,e> à <e, <e,t>>
Pg. 290, two lines above (16), “which called” à “which is called”
Pg. 290, two lines below (16), a à b (also for next line)
Pg. 290, R-8, second line, there is a box following alpha which should be deleted
Pg. 291, sixth line, (11b) à (12b),
Two lines down, “callers” à “lovers”
Pg. 292, third line down, (3) à (15)
Pg. 292, (20), first line, should be g-sup
Pg. 298, second line of definition “time”, should this be “type”?
Pg. 314, six lines under (38), “Jack” à “Bill”
Pg. 347, first and third lines under (34) and (35), theses references to (34) and (35) need letters
Pg. 372, paragraph under (12), second  line from bottom, “no fourth grade boy” à “every fourth grade boy”
Pg. 373, second paragraph, middle, there is no (12b)
Pg. 373, second paragraph, third from last line, “no fourth grade boy” à “every fourth grade boy”
Pg. 382, sixth line under 17.4.2, “senior” should be in italics
Pg. 390, first line, “with” à “when”?

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